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 

Keywords

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 ...

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