The Unimodular Intersection Problem

TL;DR

This paper demonstrates that certain intersection problems involving paths and matchings in graphs can be solved efficiently using polynomial-time algorithms, extending to unimodular set systems.

Contribution

It introduces polynomial-time solutions for the unimodular intersection problem, generalizing previous results to a broader class of combinatorial structures.

Findings

Polynomial-time algorithms for intersecting paths and matchings

Extension of results to unimodular set systems

Broader applicability in combinatorial optimization

Abstract

We show that finding minimally intersecting $n$ paths from $s$ to $t$ in a directed graph or $n$ perfect matchings in a bipartite graph can be done in polynomial time. This holds more generally for unimodular set systems.