Finding Maximal Common Subgraphs via Time-Space Efficient Reverse Search

International audienceFor any two given graphs, we study the problem of finding isomorphisms that correspond to inclusion-maximal common induced subgraphs that are connected. While common (induced or not) subgraphs can be easily listed using some well known reduction and state-of-the-art algorithms, they are not guaranteed to be connected. To meet the connectivity requirement, we propose an algorithm that revisits the paradigm of reverse search and guarantees polynomial time per solution (delay) and linear space, on top of showing good practical performance

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

A Fast Algorithm for Large Common Connected Induced Subgraphs

International audienceWe present a fast algorithm for finding large common sub-graphs, which can be exploited for detecting structural and functional relationships between biological macromolecules. Many fast algorithms exist for finding a single maximum common subgraph. We show with an example that this gives limited information, motivating the less studied problem of finding many large common subgraphs covering different areas. As the latter is also hard, we give heuristics that improve performance by several orders of magnitude. As a case study, we validate our findings experimentally on protein graphs with thousands of atoms

A functional view on constraints

SIGLETIB: RN 9844 (252) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman