This dissertation introduces the MCSPLIT family of algorithms for two closely-related NP-hard problems that involve finding a large induced subgraph contained by each of two input graphs: the induced subgraph isomorphism problem and the maximum common induced subgraph problem.
The MCSPLIT algorithms resemble forward-checking constrant programming algorithms, but use problem-specific data structures that allow multiple, identical domains to be stored without duplication. These data structures enable fast, simple constraint propagation algorithms and very fast calculation of upper bounds. Versions of these algorithms for both sparse and dense graphs are described and implemented. The resulting algorithms are over an order of magnitude faster than the best existing algorithm for maximum common induced subgraph on unlabelled graphs, and outperform the state of the art on several classes of induced subgraph isomorphism instances.
A further advantage of the MCSPLIT data structures is that variables and values are treated identically; this allows us to choose to branch on variables representing vertices of either input graph with no overhead. An extensive set of experiments shows that such two-sided branching can be particularly beneficial if the two input graphs have very different orders or densities. Finally, we turn from subgraphs to supergraphs, tackling the problem of finding a small graph that contains every member of a given family of graphs as an induced subgraph. Exact and heuristic techniques are developed for this problem, in each case using a MCSPLIT algorithm as a subroutine. These algorithms allow us to add new terms to two entries of the On-Line Encyclopedia of Integer Sequences
