More Effort Towards Multiagent Knapsack

TL;DR

This paper explores multiagent variants of the knapsack problem, extending preference aggregation rules to include Median and Best scoring functions, analyzing their computational complexity and developing faster algorithms for certain cases.

Contribution

It introduces new preference aggregation rules for multiagent knapsack problems and provides complexity analysis and improved algorithms for these variants.

Findings

Median and Best scoring functions are viable aggregation rules.

Complexity varies with parameters like voters and items.

Faster algorithms are developed for the diverse aggregation rule.

Abstract

In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns some utility to every item. They studied three preference aggregation rules for finding a subset (knapsack) of items: individually best, diverse, and Nash-welfare-based. Informally, diversity is achieved by satisfying as many voters as possible. Motivated by the application of aggregation operators in multiwinner elections, we extend the study from diverse aggregation rule to Median and Best scoring functions. We study the computational and parameterized complexity of the problem with respect to some natural parameters, namely, the number of voters, the number of items, and the distance from an easy instance. We also study the complexity of the problem under domain restrictions. Furthermore, we present significantly faster parameterized algorithms with respect to the number of voters for the diverse aggregation rule.