Welfare Loss in Connected Resource Allocation

Abstract

We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian welfare. Specifically, we introduce the concept of egalitarian (resp., utilitarian) price of connectivity, which captures the worst-case ratio between the optimal egalitarian (resp., utilitarian) welfare among all allocations and that among connected allocations. We provide tight or asymptotically tight bounds on the price of connectivity for several large classes of graphs in the case of two agents -- including graphs with vertex connectivity $1$ or $2$ and complete bipartite graphs -- as well as for paths, stars, and cycles in the general case where the number of agents can be arbitrary.

Appears in the 33rd International Joint Conference on Artificial Intelligence (IJCAI), 2024

References in corpus (7)

• Fairly Allocating Contiguous Blocks of Indivisible Items
• The Price of Fairness for Indivisible Goods
• The Price of Connectivity in Fair Division
• Contiguous Cake Cutting: Hardness Results and Approximation Algorithms
• Communication Complexity of Discrete Fair Division
• Approximate Envy-Freeness in Graphical Cake Cutting
• Egalitarian Price of Fairness for Indivisible Goods