Planar Subgraph Isomorphism Revisited

Details Planar Subgraph Isomorphism Revisited Planar Subgraph Isomorphism Revisited

2009-09-25

arxiv.org/abs/0909.4692v1

Computer Science

Data Structures and Algorithms

13 pages, 4 figures

Scientific paper

The problem of Subgraph Isomorphism is defined as follows: Given a pattern H and a host graph G on n vertices, does G contain a subgraph that is isomorphic to H? Eppstein [SODA 95, J'GAA 99] gives the first linear time algorithm for subgraph isomorphism for a fixed-size pattern, say of order k, and arbitrary planar host graph, improving upon the O(n^\sqrt{k})-time algorithm when using the ``Color-coding'' technique of Alon et al [J'ACM 95]. Eppstein's algorithm runs in time k^O(k) n, that is, the dependency on k is superexponential. We solve an open problem posed in Eppstein's paper and improve the running time to 2^O(k) n, that is, single exponential in k while keeping the term in n linear. Next to deciding subgraph isomorphism, we can construct a solution and enumerate all solutions in the same asymptotic running time. We may list w subgraphs with an additive term O(w k) in the running time of our algorithm. We introduce the technique of "embedded dynamic programming" on a suitably structured graph decomposition, which exploits the topology of the underlying embeddings of the subgraph pattern (rather than of the host graph). To achieve our results, we give an upper bound on the number of partial solutions in each dynamic programming step as a function of pattern size--as it turns out, for the planar subgraph isomorphism problem, that function is single exponential in the number of vertices in the pattern.

Affiliated with

Also associated with

No associations

Rating

Planar Subgraph Isomorphism Revisited does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Planar Subgraph Isomorphism Revisited, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Planar Subgraph Isomorphism Revisited will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-326083