Embedding Paths into Trees: VM Placement to Minimize Congestion

  • Debojyoti Dutta
  • Michael Kapralov
  • Ian Post
  • Rajendra Shinde
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)


Modern cloud infrastructure providers allow customers to rent computing capability in the form of a network of virtual machines (VMs) with bandwidth guarantees between pairs of VMs. Typical requests are in the form of a chain of VMs with an uplink bandwidth to the gateway node of the network (rooted path requests), and most data center architectures route network packets along a spanning tree of the physical network. VMs are instantiated inside servers which reside at the leaves of this network, leading to the following optimization problem: given a rooted tree network T and a set of rooted path requests, find an embedding of the requests that minimizes link congestion.

Our main result is an algorithm that, given a rooted tree network T with n leaves and set of weighted rooted path requests, embeds a 1 − ε fraction of the requests with congestion at most poly(logn, logθ,ε − 1)·OPT (approximation is necessary since the problem is NP-hard). Here OPT is the congestion of the optimal embedding and θ is the ratio of the maximum to minimum weights of the path requests. We also obtain an O(Hlogn/ε 2) approximation if node capacities can be augmented by a (1 + ε) factor (here H is the height of the tree). Our algorithm applies a randomized rounding scheme based on Group Steiner Tree rounding to a novel LP relaxation of the set of subtrees of T with a given number of leaves that may be of independent interest.


Virtual Machine Full Version Quadratic Assignment Problem Gateway Node Reachability Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Debojyoti Dutta
    • 1
  • Michael Kapralov
    • 2
  • Ian Post
    • 2
  • Rajendra Shinde
    • 2
  1. 1.Cisco SystemsUSA
  2. 2.Stanford UniversityStanfordUSA

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