Efficient Algorithms for Electing Successive Committees

TL;DR

This paper develops parameterized algorithms to efficiently solve the NP-hard problem of selecting successive committees under temporal constraints, enabling practical application of the model in realistic scenarios.

Contribution

It introduces (parameterized) algorithms that effectively address NP-hard cases of successive committee elections for moderate candidate numbers or limited time horizons.

Findings

Algorithms solve NP-hard cases in moderate scenarios

Effective for small candidate sets or short time horizons

Enhances practical usability of temporal committee election models

Abstract

In a recently introduced model of successive committee elections (Bredereck et al., AAAI-20) for a given set of ordinal or approval preferences one aims to find a sequence of a given length of "best" same-size committees such that each candidate is a member of a limited number of consecutive committees. However, the practical usability of this model remains limited, as the described task turns out to be NP-hard for most selection criteria already for seeking committees of size three. Non-trivial or somewhat efficient algorithms for these cases are lacking too. Motivated by a desire to unlock the full potential of the described temporal model of committee elections, we devise (parameterized) algorithms that effectively solve the mentioned hard cases in realistic scenarios of a moderate number of candidates or of a limited time horizon.