Subgraph Isomorphism in Planar Graphs and Related Problems

TL;DR

This paper presents a linear-time algorithm for subgraph isomorphism in planar graphs of constant size, utilizing graph partitioning and dynamic programming, and extends these techniques to various other planar graph problems.

Contribution

It introduces a novel linear-time approach for subgraph isomorphism in planar graphs and applies similar methods to multiple related problems.

Findings

Linear-time subgraph isomorphism algorithm for planar graphs.

Applicable to problems like connectivity, diameter, girth, and shortest paths.

Efficient dynamic programming technique for small tree-width partitions.

Abstract

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 connectivity, diameter, girth, induced subgraph isomorphism, and shortest paths.