Certifying Solvers for Clique and Maximum Common (Connected) Subgraph Problems

An algorithm is said to be certifying if it outputs, together with a solution to the problem it solves, a proof that this solution is correct. We explain how state of the art maximum clique, maximum weighted clique, maximal clique enumeration and maximum common (connected) induced subgraph algorithms can be turned into certifying solvers by using pseudo-Boolean models and cutting planes proofs, and demonstrate that this approach can also handle reductions between problems. The generality of our results suggests that this method is ready for widespread adoption in solvers for combinatorial graph problems

A Learning Based Branch and Bound for Maximum Common Subgraph Related Problems

34th AAAI Conference on Artificial Intelligence / 32nd Innovative Applications of Artificial Intelligence Conference / 10th AAAI Symposium on Educational Advances in Artificial Intelligence, New York, NY, FEB 07-12, 2020International audienceThe performance of a branch-and-bound (BnB) algorithm for maximum common subgraph (MCS) problem and its related problems, like maximum common connected subgraph (MCCS) and induced Subgraph Isomorphism (SI), crucially depends on the branching heuristic. We propose a branching heuristic inspired from reinforcement learning with a goal of reaching a tree leaf as early as possible to greatly reduce the search tree size. Experimental results show that the proposed heuristic consistently and significantly improves the current best BnB algorithm for the MCS, MCCS and SI problems. An analysis is carried out to give insight on why and how reinforcement learning is useful in the new branching heuristic