A new, fast algorithm for detecting protein coevolution using maximum compatible cliques

<p>Abstract</p> <p>Background</p> <p>The MatrixMatchMaker algorithm was recently introduced to detect the similarity between phylogenetic trees and thus the coevolution between proteins. MMM finds the largest common submatrices between pairs of phylogenetic distance matrices, and has numerous advantages over existing methods of coevolution detection. However, these advantages came at the cost of a very long execution time.</p> <p>Results</p> <p>In this paper, we show that the problem of finding the maximum submatrix reduces to a multiple maximum clique subproblem on a graph of protein pairs. This allowed us to develop a new algorithm and program implementation, MMMvII, which achieved more than 600× speedup with comparable accuracy to the original MMM.</p> <p>Conclusions</p> <p>MMMvII will thus allow for more more extensive and intricate analyses of coevolution.</p> <p>Availability</p> <p>An implementation of the MMMvII algorithm is available at: <url>http://www.uhnresearch.ca/labs/tillier/MMMWEBvII/MMMWEBvII.php</url></p

On Maximum Weight Clique Algorithms, and How They Are Evaluated

Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus 1. For constraint programming approaches, this rule has clear implications, favouring weight-based rather than degree-based heuristics. We show that similar implications hold for dedicated algorithms, and that additionally, weight distributions affect whether certain inference rules are cost-effective. We look at other families of benchmark instances for the maximum weight clique problem, coming from winner determination problems, graph colouring, and error-correcting codes, and introduce two new families of instances, based upon kidney exchange and the Research Excellence Framework. In each case the weights carry much more interesting structure, and do not in any way resemble the 200 rule. We make these instances available in the hopes of improving the quality of future experiments

Saving probe bits by cube domination

We consider the problem of storing a single element from an m-element set as a binary string of optimal length, and comparing any queried string to the stored string without reading all bits. This is the one-element version of the problem of membership testing in the bit probe model, and solutions can serve as building blocks of general membership testers. Our principal contribution is the equivalence of saving probe bits with some generalized notion of domination in hypercubes. This domination variant requires that every vertex outside the dominating set belongs to a sub-hypercube, of fixed dimension, in which all other vertices belong to in the dominating set. This fixed dimension equals the number of saved probe bits. We give specific constructions showing that up to three probe bits can be ignored when m is far enough from the next larger power of 2. The main technical idea is to use low-dimensional (grid) relaxations of the problem. The design of optimal schemes remains an open problem, however one has to notice that even usual domination in hypercubes is far from being completely understood