Exact Parallel Maximum Clique Algorithm for General and Protein Graphs

Abstract

A new exact parallel maximum clique algorithm MaxCliquePara, which finds the maximum clique (the fully connected subgraph) in undirected general and protein graphs, is presented. First, a new branch and bound algorithm for finding a maximum clique on a single computer core, which builds on ideas presented in two published state of the art sequential algorithms is implemented. The new sequential MaxCliqueSeq algorithm is faster than the reference algorithms on both DIMACS benchmark graphs as well as on protein-derived product graphs used for protein structural comparisons. Next, the MaxCliqueSeq algorithm is parallelized by splitting the branch-and-bound search tree to multiple cores, resulting in MaxCliquePara algorithm. The ability to exploit all cores efficiently makes the new parallel MaxCliquePara algorithm markedly superior to other tested algorithms. On a 12-core computer, the parallelization provides up to 2 orders of magnitude faster execution on the large DIMACS benchmark graphs and up to an order of magnitude faster execution on protein product graphs. The algorithms are freely accessible on http://commsys.ijs.si/~matjaz/maxclique.

LiSiCA: A Software for Ligand-Based Virtual Screening and Its Application for the Discovery of Butyrylcholinesterase Inhibitors

“…12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 3 In this article, we developed LiSiCA (Ligand Similarity using Clique Algorithm), an alignment-free LBVS algorithm and software, based on a novel two-and three-dimensional graph representation of molecules and a fast maximum clique algorithm. 13,14 LiSiCA employs all atom graph representation of compounds, in which each vertex represents one atom, in contrast to other clique-based LBVS approaches 1,15,16 that use reduced graphs, in which a vertex represents a functional group, e.g., aromatic ring, hydrogen bond donor/acceptor. Atomic-level details were achieved by using a fast maximum clique algorithm, 13,14 which enables clique searching in large graphs and is up to two orders of magnitude faster than the commonly used Bron-Kerbosh maximal clique algorithm.…”

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

“…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.…”

A parallel branch and bound algorithm for the maximum labelled clique problem

“…On the other hand, adapting a dedicated maximum clique algorithm for this problem did not require major changes. It is true that these algorithms are non-trivial to implement, but there are at least three implementations with publicly available source code (one in Java [8] and two with multi-threading support in C++ [2,5]). Also of note was that bit-and thread-parallelism, which are key contributors to the raw performance of maximum clique algorithms, were similarly successful in this setting.…”