Polynomial algorithms for open plane graph and subgraph isomorphisms

Polynomial algorithms for open plane graph and subgraph isomorphisms

Graphs are used as models in a variety of situations. In some cases, e.g. to model images or maps, the graphs will be drawn in the plane, and this feature can be used to obtain new algorithmic results. In this work, we introduce a special class of graphs, called open plane graphs, which can be used to represent images or maps for robots: they are planar graphs embedded in the plane, in which ce...

Graph layout using subgraph isomorphisms

Today, graphs are used for many things. In engineering, graphs are used to design circuits in very large scale integration. In computer science, graphs are used in the representation of the structure of software. They show information such as the flow of data through the program (known as the data flow graph [1]) or the information about the calling sequence of programs (known as the call graph...

Algorithms for Graph Similarity and Subgraph Matching

We deal with two independent but related problems, those of graph similarity and subgraph matching, which are both important practical problems useful in several fields of science, engineering and data analysis. For the problem of graph similarity, we develop and test a new framework for solving the problem using belief propagation and related ideas. For the subgraph matching problem, we develo...

The Penrose Polynomial of a Plane Graph

A polynomial graph extension procedure for improving graph isomorphism algorithms

We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by G(V,E) and G(V , E)). Thus, information from the edge structures of G and G is ”hashed” into the weighted edges of the extended graphs. A bijective mapping i...