A Unified Framework for Integer Programming Formulation of Graph Matching Problems

TL;DR

This paper introduces a comprehensive unified framework for formulating graph matching problems as integer programs, facilitating cross-disciplinary approaches and simplifying complex pattern analysis tasks.

Contribution

It provides the first comprehensive integer programming formulation for a wide range of graph matching problems, unifying diverse existing approaches.

Findings

The framework encompasses various graph optimization problems from different disciplines.

It enables easier visualization and understanding of complex graph problems.

The approach can potentially improve solution efficiency and accuracy.

Abstract

Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program and then solved using exact, heuristic, and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding complex mathematical programming problems, especially integer programs. Formulating a graph problem as a natural integer program (IP) is often a challenging task. However, an IP formulation of the problem has many advantages. Several researchers have noted the need for natural IP formulation of graph theoretic problems. The present study aims to provide a unified framework for IP formulation of graph-matching problems. Although there are many surveys on graph matching problems, none is concerned with IP formulation. This paper is the first to provide a comprehensive IP formulation for such problems. The framework includes a variety of graph optimization problems in the literature. While these problems have been studied by different research communities, however, the framework presented here helps to bring efforts from different disciplines to tackle such diverse and complex problems. We hope the present study can significantly help to simplify some of the difficult problems arising in practice, especially in pattern analysis.