The Complexity of Subelection Isomorphism Problems

TL;DR

This paper investigates the computational complexity of finding isomorphic subelections within elections, introducing new problems and analyzing their difficulty and approximation potential, with experimental insights into election models.

Contribution

It introduces the Subelection Isomorphism and Maximum Common Subelection problems, expanding the understanding of election isomorphism complexities and their practical implications.

Findings

Complexity results for the new problems

Approximation bounds and algorithms

Experimental insights into election models

Abstract

We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational complexity and approximability. Using our problems in experiments, we provide some insights into the nature of several statistical models of elections.