Leveraging an open source serverless framework for high energy physics computing

CERN (Centre Europeen pour la Recherce Nucleaire) is the largest research centre for high energy physics (HEP). It offers unique computational challenges as a result of the large amount of data generated by the large hadron collider. CERN has developed and supports a software called ROOT, which is the de facto standard for HEP data analysis. This framework offers a high-level and easy-to-use interface called RDataFrame, which allows managing and processing large data sets. In recent years, its functionality has been extended to take advantage of distributed computing capabilities. Thanks to its declarative programming model, the user-facing API can be decoupled from the actual execution backend. This decoupling allows physical analysis to scale automatically to thousands of computational cores over various types of distributed resources. In fact, the distributed RDataFrame module already supports the use of established general industry engines such as Apache Spark or Dask. Notwithstanding the foregoing, these current solutions will not be sufficient to meet future requirements in terms of the amount of data that the new projected accelerators will generate. It is of interest, for this reason, to investigate a different approach, the one offered by serverless computing. Based on a first prototype using AWS Lambda, this work presents the creation of a new backend for RDataFrame distributed over the OSCAR tool, an open source framework that supports serverless computing. The implementation introduces new ways, relative to the AWS Lambda-based prototype, to synchronize the work of functions.


Introduction
One of the main instruments needed for research and progress in the field of High Energy Physics (HEP) is the particle accelerator, the largest of which is the Large Hadron Collider (LHC). This accelerator, built and operated by the European Organization for Nuclear Research (CERN), can generate up to one petabyte (PB) of data per second while operational.
The LHC does not work constantly, the generation of the physics events is organized in runs. The third run of the LHC began in July 2022 and is scheduled to last until 2025. In addition, the LHC is scheduled for an update, called High Luminosity Large Hadron Collider (HL-LHC) [7], which will start operations in 2029 and it is estimated that it will require between 50 and 100 times more computational resources than those currently used. Figure 1 shows the computational requirements of CMS [42], one of the main experiments at the LHC. Its computational needs have been satisfied through progressive budget added to generational technological advances received year after year. However, as shown in the figure, once the HL-LHC is commissioned, these computing capabilities will fall far behind the necessary requirements [1]. Europeen pour la Recherce Nucleaire) is the largest research centre for High Energy Physics (HEP). It offers unique computational challenges as a result of the large amount of data generated by the Large Hadron Collider (LHC). CERN has developed and supports a software called ROOT, which is the de facto standard for HEP data analysis. This framework offers a high-level and CERN and many other academic institutions share resources in order to satisfy the computing requirements of the LHC experiments. Collectively, these form a grid of computing clusters called Worldwide LHC Computing Grid (WLCG) [48]. Thus, distributed computing has been a popular topic of research in the HEP field for decades. In recent years, a few key research areas have been highlighted in an R &D project [1,10,43] in order to improve the entire HEP software landscape. These efforts range from the efficiency, scalability and performance of the Fig. 1 Estimation of computational and storage requirements of the CMS experiment for the HL-LHC [1]. (The HS06 unit refers to the score obtained by a system in the HEP-SPEC06 benchmark focused on analyzing the performance of systems for tasks similar to those performed by HEP analysis [23]) 1 3 software currently used to take advantage of new architectures, to the adoption of new paradigms, such as the use of Artificial Intelligence (AI) in certain aspects of HEP or the use of Big Data models for data analysis.
In the context of data analysis, ROOT [13] is the de facto standard software framework used for storage, processing and visualization. It provides a high-level interface to data analysis, called RDataFrame [38]. This was initially developed for use on a single machine, either with one or multiple cores, but more recently it has been extended to automatically run workflows on distributed clusters by leveranging various backends, such as Apache Spark [50] or Dask [41]. The distributed extension of RDataFrame is also called DistRDF [36].
Traditional HEP distributed computing is based on batch computing systems on a managed cluster, where all the software and storage are provided by cluster administrators for the final user. Spark or Dask processing relies on the principle of infrastructure management and setting up resources on premises. On the contrary, in an unmanaged or serverless environment the users interface with abstract resources, which potentially allows even more massive parallelization across multiple machines compared to the managed approach. Furthermore, it may ease the development and deployment of parallel applications, an ongoing pain point for physics users. Thus, a serverless approach could provide a more scalable and more open alternative for HEP analysis workflows.
A first prototype of serverless backend for RDataFrame exists, that makes use of AWS Lambda [25]. Using that proposal as a starting point, this paper introduces a new serverless backend for RDataFrame based on OSCAR [40] (Open Source Computing for Data-Processing Applications). OSCAR is an open source solution that provides a self-scaling environment for serverless computing. OSCAR uses file-based events to run a High Throughput Computing model. The execution of the functions is done through the use of Docker [30] containers. This proposal provides various improvements to the model presented in the prototype backend with AWS Lambda among which we find the capability of OSCAR to be used in a cluster on-premises free of charge.
Summarizing all of the above, the novel contributions brought by this paper are: • The implementation of a new backend for distributed processing of HEP data analysis in ROOT using OSCAR . • A first study on the adaptation of the distributed computing model available so far in DistRDF to the file-based, event-driven model offered by OSCAR . • The implementation of different strategies for serverless reduction algorithms, namely an uncoordinated strategy and a coordinated one. This is precisely described in Sect. 4.2.2. • A performance evaluation of the backend implementation and the different reduction strategies, with a particular description of the different components of the workflow that may potentially add overhead to the runtime of the physics analysis.
It should be noted from this point going forward that, unlike AWS Lambda, OSCAR is an experimental tool. Thus, we state in advance in this introduction that some downsides were identified while using OSCAR that should be improved in future. At the same time, OSCAR is only an example of an open source serverless tool through which this work shows how ROOT itself can be adapted to run on various execution engines. The rest of the paper is divided as follows. Section 3 describes the two main tools used in this work. Section 4 describes the whole implementation of the backend proposed in this work. Results are shown and discussed in Sect. 5. Finally, Sect. 6 concludes the paper with some considerations for future work.

State of the art
The Function as a Service computing model (FaaS), part of the larger serverless computing paradigm, has seen a steady increase in popularity ever since its first usages by big cloud providers, first being Amazon Web Services (AWS) in 2014 [3]. This model abstracts the user from a large part of the costs associated with infrastructure management, whether on-premises or in the cloud, and its configurations. The user only needs to provide the code of the functions to execute without the need to explicitly pre-provision any type of infrastructure. For this type of services, the scaling unit is the function.
Function executions in this model are stateless (although for a few years AWS has offered the possibility for Lambda functions to have a shared and persistent file system [8]). This means that during the execution of a function, they cannot depend internally on memory, mounted disks or similar elements that in other models provide information on the state of the distributed system. Clearly, this approach can be adapted quite well to the HEP data analysis requirements described in Sect. 1.
Another feature of this model is that the functions can be executed inside a container, providing the necessary flexibility to accommodate different workflows. For instance, the container may have an environment with a ROOT installation together with any other libraries that may be needed in the analysis.
The more generic serverless computing paradigm includes other components together with the functions. For example, streaming components that generate events that will be used to trigger function invocations. Or storage systems such as Amazon S3 [5] or MinIO [31] to extract the data to be processed or store the results.
Every serverless execution engine relies on a type of abstraction layer for the infrastructure itself. This is usually provided by big vendors, such as Cloud Functions by Google [20], Lambda by Amazon [3], or open source solutions such as OpenWhisk [6] running on real or virtual machines or Knative [45] running ephemeral Docker containers directly on Kubernetes [46]. All the solutions offered by these players share many features. In some cases, communities compare the products in terms of cost efficiency and availability to make informed choices about the workflow they will propose to users. An example is offered by a recent overview of the serverless computing scenario in bioinformatics by Grzesik et al. [21]. Efficient orchestrating frameworks are useful in utilizing the power of serverless functions in data processing applications. One among these would be PyWren [24]. It allows to seamlessly distribute arbitrary Python code over multiple nodes with serverless functions. Needed objects and dependencies are serialized and sent to the Lambda execution environment in order to run the application on AWS resources natively. As of 2021, the original project is no longer maintained, but it was used as a basis for interesting extensions, including NumPyWren for numerical algebra [44]. This package provided support for distributed computation of serverless linear algebra problems on AWS Lambda, along with the development of a language, LAmbda-PACK, designed to implement highly parallel linear algebra algorithms in serverless environments. A recent alternative to NumPyWren is Wukong [16] a framework that allows the execution of jobs divided into tasks that can form complex directed acyclic graphs through a decentralized scheduler that greatly improves the features of NumPyWren.
The serverless research scenario is quite wide. Other works in this line of research are MARLA [19] (MApReduce on AWS Lambda) and SCAR [39] (Serverless Container-aware ARchitectures). MARLA is a framework that supports the MapReduce model in AWS Lambda for Python. One of the advantages of MARLA over other similar frameworks is that it is in charge of managing the entire MapReduce process, from the partitioning of the data to the generation of the final result, where the user only has to define the Map and Reduce functions of the process. SCAR is a framework that offers the possibility of executing any programming language in AWS Lambda through the use of containers, allowing the execution of any type of application in a FaaS environment, which supported this execution model before AWS itself. In particular, the use of containerized environments to run the serverless functions has become more and more popular thanks to a few key advantages it brings in terms of reproducibility and ease of deployment. But this also comes with issues to be addressed. Bila et al. [9] discuss how containers may hide vulnerabilities which can be exploited at runtime. Li et al. [28] present the benefits of reusing the same container for multiple serverless functions to avoid cold startups. Oakes et al. [34] go as far as implementing a new container runtime especially aimed at serverless workflows to obtain factors of speedup with respect to using Docker.
Serverless workflows are not a common topic in High Energy Physics literature. A recent review has highlighted a few motivations that would make the FaaS model applicable to the online trigger systems employed by LHC experiments [33]. This paper theorizes that inference using neural networks could be triggered by the events streaming from the accelerator. A more concrete example is provided by a paper related to CernVM-FS (CVMFS) [11], a file system that provides the software distribution backbone for collaborations in the field. The paper describes advances in the publishing system of the software distributions. The default model has a single server node responsible for the compilation of all the libraries and only upon a commit from this machine the distribution would be actually published and replicated. The envisioned changes would have any machine enabled with CVMFS publish the changes to cloud storage (e.g., Amazon S3) through a gateway serverless function [12]. Regarding the data analysis use case, a good example of serverless engine is provided by Lambada [32], that adds facilities on top of AWS Lambda to steer the serverless functions and shows a costefficient usage of the resources.
The contribution of this work aims at furthering the knowledge of the FaaS paradigm applied to the HEP data analysis use case. With respect to the literature reviewed, the execution backend based on OSCAR can provide an open platform for research in this field and potentially offer physicists a simple to use and cost-effective solution.

Tools
The two main software tools used in this work are ROOT and OSCAR . The integration of a C++ framework, such as ROOT into a serverless ecosystem brings a few challenges like its packaging and the instrumentation of the C++ code within a serverless function invocation. This section highlights the different aspects that are relevant to this study when using these two key tools.

ROOT
ROOT is a software developed at CERN for the analysis of high energy physics data (HEP). This software has been updated since its initial conception in 1994, expanding its functionality and adapting to new technologies. It is made up of several object oriented components that allow efficient management and analysis of large volumes of data.
One of the most important features of ROOT is its solid and flexible I/O layer. Users can write to disk any type of C++ object, including custom classes, in a compressed binary format managed by the TFile class. It is common to find in a TFile all the most important objects needed for HEP statistics, such as histograms, which in ROOT are implemented with the TH1 class. When mentioning physics datasets, the traditional ROOT implementation is done with the TTree class. This is a flexible container that can also store any type of C++ object, organizing its contents in columns (usually called branches). Different branches can be read independently, making TTree a truly columnar data format implementation. A TTree is stored on disk via the TFile class as well and multiple trees can be joined together either vertically or horizontally to create a larger dataset. Most notably, a ROOT file can be read remotely via protocols such as HTTP or XRootD [18].
Another relevant feature for this work is the presence of a C++ interpreter, called cling [47], and dynamic Python bindings based on the cppyy [26] library. These two together offer the possibility for higher-level tools like RDataFrame to provide users with modern, ergonomic interfaces that can interact with other common data science libraries, which most often offer Python APIs.

RDataFrame
RDataFrame is the high-level data analysis interface offered by ROOT. Compared to the more traditional imperative programming model, RDataFrame offers a lazy and declarative model inspired by other popular libraries such as Spark [50] or pandas [29]. It supports many types of input data formats, the most used one is TTree but for example also CSV files and numpy [22] arrays can be processed.
The declarative model has the clear advantage of taking away responsibility from the user, who only needs to declare the desired operations on the dataset, allowing for under-the-hood optimizations in the processing and I/O scheduling. The lazy approach used by the API means that the execution of the requested operations only starts when the final results are queried in the application, for example when a histogram is drawn for the first time.
The data generated by the physical events are statistically independent, so RDa-taFrame is able to abstract from the different underlying data structures in which these events are stored. This also means that parallelism can be achieved by splitting the input dataset in different groups of events and applying the computation graph to events in parallel. RDataFrame allows users to leverage all cores of their laptop with an implicit parallelism machinery based on Intel Threading Building Blocks (TBB) [37], but also to distribute the same workload to multiple machines transparently. The latter feature will be further discussed in the next section.

Distributed RDataFrame
One of the latest features introduced by the ROOT team for RDataFrame is the ability to distribute user applications to computing clusters without changing the analysis code. This is done via a thin Python layer that wraps the RDataFrame computation graph and sends it to the remote nodes leveraging popular execution engines like Spark and Dask. Such layer is called distributed RDataFrame or DistRDF. Listings 1 and 2 show how the user analysis can be run distributedly with minimal code changes.
Leveraging an open source serverless framework for high energy… Workload distribution follows the MapReduce [17] scheme: a mapper task has to apply the full set of operations requested by the user on a certain range of entries of the dataset, a reducer task needs to combine the partial outputs of two mapper tasks. Once all the results have been combined into one final result, this is sent back from the computing cluster to the user. This saves a lot of time for the analyst, who does not need to take care of merging partial results of different mapper tasks on their own as it used to happen with the traditional batch computing approach.
A fundamental feature of the distributed RDataFrame tool is the automatic splitting of the input dataset in multiple logical partitions, so that each one can be processed independently in different tasks. This splitting is done on the client side, when the user asks for the results of their operations the first time. At this moment, the only information available is the list of files that the user wants to process. In general, the number of partitions can be either provided by the user or a default value is used. The default value is the total number of cores available in the cluster. As many "approximate tasks" are created as the number of partitions indicated, the tasks are approximate since the files are only accessed once a mapper task starts on a remote node, never by the client. This is done to avoid unnecessary remote I/O which is a notorious source of performance bottlenecks for a physics analysis.
DistRDF implements a few backends that have been used as a reference for the development of this work. The following are currently supported and featured in ROOT releases: 1. Apache Spark [50]. A framework whose goal is large-scale data processing using MapReduce. It can be mounted on top of existing Apache Hadoop clusters or on its own, and the main advantage over Hadoop is that intermediate data storage is done in memory instead of disk, providing much faster speed than Hadoop. 2. Dask [41]. A Python library for parallel computing, consisting of two main elements: a dynamic task scheduler optimized for interactive workloads and support for Big Data data structures. In addition, it also offers capabilities for distributed computing in Python.
As already stated in Sect. 1, a previous study also developed a prototype implementation of a backend for DistRDF that makes use of AWS Lambda. The approach taken in that work was to invoke all the Lambda functions synchronously from the client application, using Python multithreading. This was done to be able to check the status of the invocations and retry their execution in case of error. Once all the functions had finished without errors, the reduction of the results was carried out locally on the user side. This work provides various improvements with respect to the prototype just described. For example, the client side is completely decoupled from the rest of the architecture, avoiding the need for synchronous calls to functions. Furthermore, the reduction phase is completely carried out remotely in the computing cluster, thus avoiding possibly heavy network transactions sending the partial results from the remote nodes to the client. Although these improvements are developed for OSCAR , they could be implemented also in other serverless environments.

OSCAR
OSCAR focuses on file processing by supporting a High Throughput Computing model. The execution of the functions is done through the use of Docker containers. an OSCAR installation is based on a Kubernetes cluster that is deployed using the following tools: EC3 [14] to provide horizontal cluster elasticity; Infrastructure Manager, IM [15], to support multi-cloud deployment; and CLUES [2] to manage the elasticity of the cluster by taking care of the scale in and scale out of the nodes in the cluster, based on job demand. In Fig. 2 you can see how these services interact for the deployment and scaling of the cluster.

Main components
The main components of OSCAR that affect the backend for ROOT are: • OSCAR Manager. The core of OSCAR , in charge of managing the services and the interconnection with the rest of the components. It provides a REST API for service creation. This is characterized by stateless client-server communication through the HTTP protocol. A client with the necessary credentials may consult, create, modify or delete services via the API. OSCAR also provides other forms of interaction a web interface and a command line tool, named OSCAR-CLI. 1 • Serverless Backends. OSCAR offers two possibilities for implementing the FaaS part of the Kubernetes cluster, namely, OpenFaaS [27] and Knative [45]. They support synchronous calls to services and invocation via calls to a REST API. For this work we will not use these functionalities and we will focus on the default functionality of uploading files that invoke the services asynchronously, thus generating Kubernetes jobs for the processing of files.
• Internal storage service. The cluster uses an object storage system named MinIO. The operation of this type of system is based on the creation of buckets, or repositories, in which files of any type are uploaded. These files do not have directory hierarchies like traditional file systems. Often, prefixes are used to simulate a directory structure and to maintain a certain order within a bucket. The term directory or folder is used as a concept for practical purposes [4]. These buckets provide certain features such as access control, auditing or versioning, among others. Any modification of a bucket will be sent to OSCAR as an event.
Depending on the configured rules, OSCAR will launch, or not, a service associated with that object. The results of the process can be stored directly within the service. Alternatively, they can be sent automatically to external providers such as MinIO, Amazon S3 or ONEDATA [35].

Workflow
OSCAR 's basic units of work are functions, also called services. For each service it must be defined the required resources, i.e., CPU 2 and memory; the Docker image to use as the runtime environment; the script that will be executed inside the container as an entry point and, finally, which bucket should listen for the generation of events that are created when objects are uploaded, modified or deleted. For a given bucket a prefix or suffix can be used to filter which objects will trigger the execution of the associated service. These prefixes or suffixes do not allow the option of using wildcards and must be specific. When a service is defined, OSCAR automatically takes care of generating the corresponding buckets in MinIO, as well as configuring the types of events it will listen for. The results generated by the services can be stored back on the cluster's internal MinIO server, allowing multiple services to be chained together if desired. Special care must be taken not to generate recursive loops, since no tools are provided to detect them and, in the case of a public cloud deployment, it could generate considerable costs.
OSCAR focuses on a file-driven approach. When a user uploads a file, this generates an event that is picked up by OSCAR . OSCAR then takes care of launching a job for that file by generating a Kubernetes job, that is, launching a container based on the image provided by the client. In this job the file that has triggered the service will be injected in addition to executing a script that contains the operations to be carried out, also defined by the user.

Implementation of the backend
The implementation of the backend consists of two blocks. On the one hand, the interaction between DistRDF and OSCAR is defined. On the other hand, the implementation defines how the backend schedules resources, distributes the load and collects the final result. We begin with the part related to the backend (Sect. 4.1) to continue later with the description of OSCAR services (Sect. 4.2) necessary for the satisfactory execution of the analysis.

The ROOT backend
When an analysis is performed, all the actions defined in the RDataFrame are stored without being executed. When an operation that generates output is added, e.g., generating a histogram, DistRDF takes care of parsing all the code provided by the user and passing it to an internal function, called ProcessAndMerge.
The backend features the following three objects: Mapper: Mapper: Function to be applied to each record in the specified dataset. It receives an object of type range as input and generates as output another object corresponding to the output generated by applying the Mapper function to that range, which will be referred to as a partial result. Ranges: Is a list equal in size to the number of partitions specified for analysis. Each element of the list contains the information corresponding to the data to be processed, both the source of that data and the "approximate tasks" of each of the sources. These tasks are used to get the exact events to be processed. Reducer: Is the aggregation function that will be used to reduce two by two the partial results generated by the Mapper in order to obtain the final result.
The implementation of the backend corresponding to the execution of the analysis must be carried out within function ProcessAndMerge since the value that this function must return is the result of adding all the partial results generated and it does not make sense to carry it out in another place. Somehow, all this information received by the ProcessAndMerge function has to be sent either to the OSCAR internal storage system or passed directly to the services so that not only one experiment can be run in parallel on multiple nodes but multiple users can be served concurrently by the cluster running OSCAR .
On this basis, for the integration with OSCAR an experiment can be carried out in a bucket or can be carried out in the folder 3 of an already existing bucket belonging to a specific user. The option in which a bucket represents an experiment has been chosen for simplicity, but the term root directory will be used as a generic concept to demonstrate that both implementations could be carried out, the root directory being, in the first case the name of the bucket itself and, in the second case, the root directory denoting a bucket folder. To identify an experiment, a universally unique identifier (UUID) is generated during the creation of the RDataFrame abd then used as the name of the root directory.
During preliminary tests performed in this evaluation, no performance difference was found between using a single bucket with a folder hierarchy and using multiple buckets. The difference relates to configuration issues, certain properties and permissions. Therefore, the final decision on the configuration should be relegated to the requirements of the specific cluster deployment.
In order to send these objects from the client to a remote host, they all need to be serialized. We used cloudpickle, 4 a library which extends the basic functionality of the standard Python serialization library (pickle), which allows to send defined functions during the backend execution, something that the pickle tool by itself does not support. Therefore, both the Mapper and the Reducer functions are serialized, and they all are written to a folder in the root directory of the Object Storage System (OSS) called functions. None of these scripts launch any service. With this information already in the cluster, the backend of ROOT only has to define a way to invoke the necessary services and wait for the result.
Once invoked these services, the function remains blocked and waiting for the final result. The final result can be written either to an external provider such as MinIO, Amazon S3, or ONEDATA , or to the cluster's own internal system. In our implementation, we have used the OSCAR internal system, i.e., MinIO, to store the final result. MinIO offers a function that allows to receive notifications of certain events, e.g, writing or modifying files in a specific location when they are generated. With this functionality, the client will stay on hold, avoiding a constant polling of the system.

OSCAR services
A minimum of two OSCAR services need to be created, a Mapper and a Reducer. Additionally, we may need a coordination service depending on the way the reduction is performed. At its current state, OSCAR does not support usage of wildcards in the path specified to MinIO when creating a service. Thus, supporting common use cases such as multiple users running their analysis or a single user running more than one application requires two extra steps. First, the exact path where the service will be listening for events must be specified during its creation. Second, each service needs to be destroyed, together with the data it exchanged with the OSS, once the analysis has completed successfully.

The Mapper service
For the Mapper we define a service that listens file-creation events in the mapper-jobs folder of the root directory. The backend writes in the OSS as many files as enumerated in the Ranges list. Each one of those files will have the information, serialized, of the particular range, launching thus the execution of as many concurrent Mapper services as specified at the initialization of the RDataFrame. Invoking a Mapper service consists of reading from the OSS the Mapper function. The backend deserializes the function, turns it into an object and applies it to its assigned range of entries. The access to MinIO storage system is protected with credentials so, to obtain the Mapper function, it is necessary to have access to these credentials and the path to the file that contains the Mapper function.
When a Mapper has finished processing the analysis part, it writes the result returned by the Mapper function in a temporary file of the container, following the philosophy of OSCAR , so that it is in charge of managing the upload of those results to MinIO. OSCAR will write this result to the partial-results folder, which will trigger the reduction process. This event will or will not directly launch another service, depending on the reduction model used.

The Reducer service
The reduction phase is much faster than the map phase, since it simply consists of merging partial results and there are no complex computations involved. Nonetheless, performing the reduction in a stateless scenario is not a trivial problem. Compared to a traditional MapReduce workflow, there is no central scheduler that can decide when the reduction phase should start and how the reducers should be run. Thus, this work proposes two ways of performing this phase: • Uncoordinated Reduction. Under this model of coordination, the result written by each Mapper will launch a Reducer. The problem of a reduction in a serverless environment without coordination or uncoordinated lies on how to check the state of the operation. The mapping process will generate a given set of partial results. If we set an order in the Mapper services invoked assigning an identifier to each one of them, lets say, the rank in the list of range, limiting the reduction to be done in a given order, the reduction can be carried out without the presence of a coordinator "manager". Each partial result needs to know which other partial result it should be reduced with. This additional information, necessary for this solution to work, can be found in the reducer-jobs folder. This folder contains as many files as reduction jobs. The files names are selected according to the reduction process. For instance, let there be two Mappers with identifiers 1_1 and 2_2, respectively, then the name of the fale representing their reduction is 1_1-2_2. A Mapper, upon completion, performs the reduction if the data of its counterpart is available in the file system. Otherwise, simply stores the partial result, that will wait for the other mapper to finish. It is necessary to find a way to determine the generation of the Mapper names in a deterministic way so that whatever be the number of Mappers invoked, the reduction is carried out successfully. The algorithm proposed to solve this problem focuses on generating a binary tree from the leaves to the root, in which the leaves are the identifiers of the Mappers, and at each level from bottom to top the names are combined two by two until reaching the root node. The name combination is done by taking the identifiers of the extremes that will match the minimum and maximum identifiers that have been reduced up to that point. For their part, the Reducer must write in partial-results the result with the name corresponding to the reduction of the two reduced jobs so that the new Reducer that is invoked is able of reducing itself with another partial result. This generation of reduced jobs is built into the backend of ROOT but has been developed in this section for convenience. This idea can be easily generalized to non binary trees. We show a reduction example in Fig. 3 assuming a division of the analysis load into 8 parts.
In these trees, the nodes of the deepest level will be discarded since they correspond to the Mappers and will write the name to the corresponding folder. The main advantage of this approach is that we can get rid of a manager process or a coordination function that should permanently be monitoring the process, with the consequent waste of resources, which is very discouraged on platforms, such as AWS Lambda. On the contrary, there exists a disadvantage. If two Mappers that are to be reduced together terminate and write their partial result nearly at the same time, they both will check that their counterpart already wrote a partial result in their corresponding file. In consequence, both Mappers will probably perform the same reduction at the same time. This fact, although produces a correct final result, also produces in turn a performance penalty. Figure 4 shows a schema of the uncoordinated reduction process. • Coordinated reduction: Another alternative consists of using an additional service, i.e., a coordination process which is in charge of the whole reduction process. The backend invokes this service once, at the starting. This service monitors the Mappers once they are created and the folder where they write the partial results (partial-results). The monitoring process is done similarly as the client does when waits for the final result, receiving an event by the time a partial result is written in the file. The coordination service is responsible of launching reduction jobs when necessary and of writing in the folder reducer-jobs the work to be done. On the one hand, the backend will generate a file with the necessary configuration of the coordinating service. This configuration consists of a list of integers where each value represents the number of partial results that should be merged once a Reducer is invoked. The coordinator watches the folder in which the partial results are written and, upon notification of a new result, it will save the name of the given file. Once the number of partial results corresponding to an element of the configuration list is reached, the coordinator will generate a reduction job including the names of all the partial results that should be merged. Once done, it will pass to the next element in the reduction list. An optimization carried out during this work is that the last reduction job is performed directly by the coordinator service, so that no extra time is spent waiting. It should be noted that since the Reducer function only accepts two input parameters, these "multiple" reductions are performed by iterating over the jobs to be reduced, but they avoid invoking multiple Reducers and some of the limitations of the uncoordinated reduction approach. Writing the jobs Fig. 4 Component interaction in the uncoordinated reduction process. Numbers denote events order is done by the coordinator directly to MinIO without interference from the normal OSCAR workflow. In fact, usually OSCAR only uploads files once a service has terminated. But the coordinator service should not finish until all the MapReduce workflow has ended. In this case the Reducer will be called when the files are written to the reducer-jobs folder instead of partial-results folder, as it was in the uncoordinated case. The reduction service needs an additional modification. There is no longer need to check whether there are other partial results pending. There is only need to deserialize the content of the job, get the partial results from MinIO and reduce them all. Once it has finished reducing them, it will write that partial result to a file with the result that OSCAR will upload to MinIO, finally triggering a notification to the coordinator. With the coordinated reduction is not necessary to keep the order of the file names. Indeed, the coordinator can structure the process of reduction as convenient, e.g., into two parts or choosing an imbalanced splitting (80-20%). Figure 5 shows a schema of the coordinated reduction process.

Summary of the backend
Preliminary attempts of integrating the backend with OSCAR tried using the OSCAR API to call the Mapper and Reducer services. The final implementation instead accesses directly the files on MinIO to generate events. This choice conveniently provides the possibility to resume the execution at any point of failure during the MapReduce workflow. Another difference between the two models is that in the uncoordinated reduction the jobs are written before the Mappers start whilst in the coordinated one the jobs are written by the coordinator when necessary.
One of the current requirements of this backend is the need to define the number of Mappers to be invoked for the analysis. In other backends it is possible to obtain the number of cores of the cluster but, in OSCAR , this information is not available at the time the services are created. In fact, the whole serverless approach relies on the idea that users can scale the number of function calls automatically depending on the amount of work provided. A possibility for future research would be to attempt at predicting the best number of functions that should be invoked, based on the workload given by the user application.

Experiments
One of the most important performance metrics for a HEP analysis is the so-called time-to-plot. That is, the time elapsed between the moment a user starts the analysis and the moment they can see a plot of the results on their screen. This metric determines the real scalability of the implementation of the proposed backends.
The experiments that will be described in this section all have to go through the usual two stages of the MapReduce scheme, plus some extra scheduling and orchestration that is more specific to OSCAR . Figure 6 shows the stages of the process where the blue squares represent the work being done outside of the physics analysis, such as container start and kill, MinIO iteration and others. The red squares correspond to the time devoted to the analysis itself. In order to obtain this information the code of the OSCAR services is wrapped with a Python script that invokes the mapper or reducer functions and monitors the hardware resources and time spent executing. Leveraging an open source serverless framework for high energy…

Setup
A total of 6 working nodes were made available for the purposes of this work. Each working node is a virtual machine hosted on a OSCAR -enabled computing cluster, located in Valencia (Spain). The underlying hardware is described in Table 1. Each OSCAR service created, i.e., the mapper and the reducer, is configured to invoke functions with 1 vCPU and 3 GB of RAM available.

Methodology
Two types of analysis were employed as benchmarks in this work. The first type is a real physics analysis, processing data from events recorded by the CMS experiment in 2012 to finally plot a histogram of the di-muon mass spectrum [49]. The amount of data for this experiment consists of 200GB obtained from replicating one hundred times the original dataset file of 2GB. This analysis was carried out with two types of benchmarks, differing for the location of the dataset at runtime: either stored in the CERN data center or in the MinIO storage attached to the OSCAR cluster, much closer to the computing nodes.
The second type of analysis consists of a simulated workload that reads no data from disk or network and can better highlight the best CPU usage the backend can drive. A simulated dataset is created at runtime in-memory, with roughly the same amount of data that would be processed in the other type of analysis. The Mapper of this experiment will generate the required data locally and will apply a series of operations over the data.
For each of the three experiments, an increasing number of splits of the input dataset (also called partitions) was studied : 1, 2, 4, 8, 16, 32, 48, 64, 80. Each split corresponds to one mapper task, thus one invocation of the corresponding OSCAR service, which are then all executed simultaneously on the available nodes. The overall number of cores in the cluster would be 96, but in each node the Kubernetes service consumes a small amount of CPU thus hindering performance when all cores of a single VM are used. For this reason, the 96 partition count is omitted Cluster public network 10GbE MinIO The object storage system is hosted on a dedicated disc with the following performance: 3500MB/s sequential read and 3000 MB/s sequential write The Docker images are downloaded to the cluster before the experiments are run to avoid fetching the 4GB sized images during the first experiment.

Results
In Fig. 7 the time-to-plot for all the experiments can be observed. As expected, the experiment with the data located within the cluster is faster than the experiment with the data located at CERN's servers.
In Fig. 8, the speedup for all the experiments is shown alongside the optimal speedup that should be expected from this kind of analysis, as all the data to be processed are independent. For the experiments that use real data we can observe that CERN outperforms the data stored in MinIO, something that should not happen unless hitting some bottleneck with the disk where MinIO is operating. This assumption is based on the fact that MinIO storage is placed within the  Leveraging an open source serverless framework for high energy… same network and the same machines that run the OSCAR services. Thus, latency should be minimal and I/O throughput should be higher than reading remotely from CERN, due to the geographical distance.
For the CERN experiment, when we use 48 Mappers or more, the speedup remains constant, being probably a network bottleneck. Similarly, also the simulated workload shows a poor performance scaling, reaching less than half of the optimal speedup as the core count increases.
Regarding the CPU and Memory utilization, Fig. 9 shows the expected behavior. The simulated workload has a CPU usage close to 100% and the experiment with the data stored in MinIO also makes a better usage of the CPU as it has to spend less time waiting for the data to arrive due to its locality. Looking at Fig. 10 we can see that none of the experiments is close to reaching the 3GiB memory limit set, so we can discard this limit as a reason for the poor performance.
In order to better investigate the lack of scaling, the focus is shifted to the simulated workload. The other applications that read data may be influenced by I/O with the network or the local filesystem, so it is preferable to have a fully CPU bound workload to avoid any noise from other factors. Table 2 describes the difference in time between the fastest Mapper and the slowest one for the simulated workload.  In this workload the difference should be within a reasonable margin (e.g., 2-3%), which may be justifiable due to noise on the system, but we can see that the difference in time reaches up to 29.45% . Figure 11 shows this information graphically. The same workload was run with distributed RDataFrame outside of the OSCAR cluster, on a single physical machine. The difference in time between the fastest and the slowest Mapper in this controlled condition is on average 3% . With this information we can conclude that there are unknown sources of bottlenecks coming from the OSCAR cluster.

Comparison between reduction strategies
The previous results were relative to the uncoordinated reduction strategy. Section 4 introduced another possible way of addressing the reduction phase, which is further discussed in this section and compared to the first one.
In the uncoordinated reduction the degree of the tree is fixed to two. The coordinated reduction model is more flexible. Taking as a starting point the overhead introduced by OSCAR , we will focus on a two step reduction. This means that the coordinator will launch a reduction service to merge a determined amount of partial results, while the remaining partial results will be merged by the coordinator itself. For this coordinated reduction three different configurations of load partitioning have been studied: • 0% : all the reductions are performed by the coordinator. • 50% : the invoked reducers process 50% of the reductions and the remaining reductions are performed by the coordinator • 87.5% : the reducers are invoked for 87.5% of cases, the coordinator performs the remaining 12.5%. Table 3 shows the results for this fine-tuning, all the configurations have similar results and the differences can be attributed to the runtime variability of the various mappers. For the comparison with the uncoordinated reduction the 87.5% will be used.
For this fine-tuning experiment the tests have been carried out using 80 Mapper services as it generates the biggest amount of reductions required. Figure 12 shows that, despite the variability of the system, the coordinated reduction is faster than the binary reduction, and this difference increases with the amount of Mappers. This is due to the fact that for the uncoordinated reduction, the last Mapper service to finish has to travel the entire path to the root of the tree invoking a service on each step and the greater the amount of Mappers the deeper the tree. This could be partially solved if instead of performing only one reduction in the uncoordinated reduction, the Reducer also checks if it can perform any other reduction in the path to the root.

Conclusion
In this work we have extended the functionality of ROOT with another serverless engine that improves some of the shortcomings of the previous one based on AWS Lambda. The open-source platform provided by OSCAR is a solid basis for a new DistRDF backend that could be used by physicists to easily deploy their distributed environments. A few areas of improvement were found for OSCAR , in particular regarding the asynchronous function invocations, which rely on the underlying Kubernetes batch job scheduler. The experimental results still favor the current distributed backends offered via Spark and Dask. Nonetheless, the serverless approach is one of the best options to afford the necessary scalability requested by future HEP computing needs. In that regard, this work paves the road to addressing this challenge.

Declarations
Conflict of interest Financial interests are disclosed in Funding. The authors declare no other competing interest for this work.

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