PTAS for Minimax Approval Voting

TL;DR

This paper presents a Polynomial-Time Approximation Scheme (PTAS) for the minimax approval voting problem, effectively minimizing the maximum Hamming distance in committee selection, resolving an open question in the field.

Contribution

It introduces a PTAS for the minimax approval voting problem, adapting techniques from the Closest String problem to improve approximation guarantees.

Findings

Provides a PTAS for minimax approval voting

Resolves an open problem from prior research

Adapts structural techniques from Closest String problem

Abstract

We consider Approval Voting systems where each voter decides on a subset to candidates he/she approves. We focus on the optimization problem of finding the committee of fixed size k minimizing the maximal Hamming distance from a vote. In this paper we give a PTAS for this problem and hence resolve the open question raised by Carragianis et al. [AAAI'10]. The result is obtained by adapting the techniques developed by Li et al. [JACM'02] originally used for the less constrained Closest String problem. The technique relies on extracting information and structural properties of constant size subsets of votes.