Donald Bren School of Information and Computer Sciences

We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic programming within each piece. The same methods can be used to solve other planar graph problems including diameter, girth, induced subgraph isomorphism, and shortest paths. We also extend our techniques to other families of graphs including the graphs of bounded genus.