Living Reference Work Entry

Encyclopedia of Algorithms

pp 1-4

Date: Latest Version

Distributed Computing for Enumeration

  • Alexandre TermierAffiliated withLIG, Université Grenoble Alpes Email author 


Enumeration Parallelism Multicore Cluster Work sharing Work stealing

Years and Authors of Summarized Original Work

2006; Buehrer, Parthasarathy, Chen

2012; Martins, Manquiho, Lynce

2014; Negrevergne, Termier, Rousset, Mehaut

Problem Definition

This entry considers enumeration of combinatorial problems, which can be formulated as follows. Given a large search space \(\mathcal{C}\) and a predicate of interest \(P : \mathcal{C}\mapsto \left \{\mathrm{true},\ \mathrm{false}\right \}\) the goal is to enumerate the solutions \(\mathcal{S}\subseteq \mathcal{C}\) such that \(\forall ?s \in \mathcal{S}\quad P\left (s\right ) =\mathrm{ true}\). In most settings,\(\mathcal{C}\) is the complete set of combinations of an initial set \(\mathcal{G}\); hence,\(\left \vert \mathcal{C}\right \vert = 2^{\left \vert \mathcal{G}\right \vert }\) and the problem is NP-hard. There are also cases where the elements to enumerate are not sets but other combinatorial structures such as sequences or graphs.

We restrict ourselves to the case where ...

This is an excerpt from the content