The Shape of the Search Tree for the Maximum Clique Problem and the Implications for Parallel Branch and Bound

McCreesh, Ciaran; Prosser, Patrick

doi:10.1145/2742359

Cited by 31 publications

(38 citation statements)

References 47 publications

(59 reference statements)

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“…ZRAM is a general-purpose framework that is able to handle a number of other applications, such as branch-and-bound and backtracking, for which there are by now a large number of competing frameworks. Recent papers by Crainic et al [25], McCreesh et al [50] and Herrera et al [38] describe over a dozen such systems. While branch-and-bound may seem similar to reverse search enumeration, there are fundamental differences.…”

Section: Other Parallel Codesmentioning

confidence: 99%

mplrs: A scalable parallel vertex/facet enumeration code

Avis

Jordan

2017

Math. Prog. Comp.

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We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the existing lrs code with only minor modifications. mplrs was derived from the earlier parallel implementation plrs, written by G. Roumanis in C++ which runs on a shared memory machine. By improving load balancing we are able to greatly improve performance for medium to large scale parallelization of lrs. We report computational results comparing parallel and sequential codes for vertex/facet enumeration problems for convex polyhedra. The problems chosen span the range from simple to highly degenerate polytopes. For most problems tested, the results clearly show the advantage of using the parallel implementation mplrs of the reverse search based code lrs, even when as few as 8 cores are available. For some problems almost linear speedup was observed up to 1200 cores, the largest number of cores tested.

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Section: Other Parallel Codesmentioning

confidence: 99%

mplrs: A scalable parallel vertex/facet enumeration code

Avis

Jordan

2017

Math. Prog. Comp.

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“…Maximum clique algorithms have been extended for thread-parallel search [10,28,44], and in particular, work stealing strategies designed to eliminate exceptionally hard instances by forcing diversity at the top of search [30] could be beneficial in eliminating some of the rare cases where the clique algorithm is many orders of magnitude worse than the CP models. On the CP side, the focus for parallelism has been on decomposition [33], rather than fully dynamic work stealing-it would be interesting to compare these approaches.…”

Section: Resultsmentioning

confidence: 99%

“…Thus we re-evaluate the approach using a modern maximum clique algorithm. Association graphs are dense, even if the input is sparse, so we will using (the single-threaded, bit-parallel version of) the maximum clique solver by McCreesh and Prosser [30], which implements Prosser's [38] "MCSa1" variant of a series of algorithms due to Tomita et al [51][52][53], using a bitset encoding due to San Segundo et al [45,47]. We compare this to the "FC+Bound" and "MAC+Bound" (simply referred to as FC and MAC) CP implementations of Ndiaye and Solnon [34], using smallest domain first for variable ordering, and a value ordering which prefers vertices of most similar degree.…”

Section: Re-evaluating the Clique Model For Mcsmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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Abstract. The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

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“…We give a brief overview here. Recent papers by Crainic et al [17], McCreesh et al [37] and Herrera et al [25] describe over a dozen such systems. While branch and bound may seem similar to reverse search enumeration, there are fundamental differences.…”

Section: Survey Of Previous Workmentioning

confidence: 99%

mts: a light framework for parallelizing tree search codes

Avis

Jordan

2019

Optimization Methods and Software

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We describe mts, a generic framework for parallelizing certain types of tree search programs including reverse search, backtracking, branch and bound and satisfiability testing. It abstracts and generalizes the ideas used in parallelizing lrs, a reverse search code for vertex enumeration. mts supports sharing information between processes which is important for applications such as satisfiability testing and branch-and-bound. No parallelization is implemented in the legacy single processor programs minimizing the changes needed and simplying debugging. mts is written in C, uses MPI for parallelization and can be used on a network of computers. We give four examples of reverse search codes parallelized by using mts: topological sorts, spanning trees, triangulations and Galton-Watson trees. We also give a parallelization of two codes for satisfiability testing. We give experimental results comparing the parallel codes with other codes for the same problems.

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The Shape of the Search Tree for the Maximum Clique Problem and the Implications for Parallel Branch and Bound

Cited by 31 publications

References 47 publications

mplrs: A scalable parallel vertex/facet enumeration code

mplrs: A scalable parallel vertex/facet enumeration code

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

mts: a light framework for parallelizing tree search codes

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