# Using Matching to Detect Infeasibility of Some Integer Programs

## TL;DR

This paper introduces a matching-based heuristic algorithm for detecting infeasibility in certain zero-one integer programs, demonstrating its application to Hamilton cycle and isomorphism problems with potential for parallel processing.

## Contribution

The paper presents a new matching heuristic algorithm that detects infeasibility in formulated zero-one IPs, adaptable to complex problems and parallel implementation.

## Key findings

- Successfully applied to infeasible Hamilton cycle instances
- Modeling of graph and subgraph isomorphism problems for the algorithm
- Algorithm designed for parallel processing and extensibility

## Abstract

A novel matching based heuristic algorithm designed to detect specially formulated infeasible zero-one IPs is presented. The algorithm input is a set of nested doubly stochastic subsystems and a set E of instance defining variables set at zero level. The algorithm deduces additional variables at zero level until either a constraint is violated (the IP is infeasible), or no more variables can be deduced zero (the IP is undecided). All feasible IPs, and all infeasible IPs not detected infeasible are undecided. We successfully apply the algorithm to a small set of specially formulated infeasible zero-one IP instances of the Hamilton cycle decision problem. We show how to model both the graph and subgraph isomorphism decision problems for input to the algorithm. Increased levels of nested doubly stochastic subsystems can be implemented dynamically. The algorithm is designed for parallel processing, and for inclusion of techniques in addition to matching.