arXiv subjects

Shengwei Zhou

Publications and source records attributed to Shengwei Zhou.

23 records · Page 2Linked to original sources

arXiv2023

Approximately EFX Allocations for Indivisible Chores

In this paper, we study how to fairly allocate a set of m indivisible chores to a group of n agents, each of which has a general additive cost function on the items. Since envy-free (EF) allocations are not guaranteed to exist, we consider the notion of envy-freeness up to any item (EFX). In contrast to the fruitful results regarding the (approximation of) EFX allocations for goods, very little is known for the allocation of chores. Prior to our work, for the allocation of chores, it is known that EFX allocations always exist for two agents or general number of agents with identical ordering cost functions. For general instances, no non-trivial approximation result regarding EFX allocation is known. In this paper, we make progress in this direction by providing several polynomial time algorithms for the computation of EFX and approximately EFX allocations. We show that for three agents we can always compute a 4.45-approximation of EFX allocation. For n>=4 agents, our algorithm always computes a (3n^2-n)-approximation. We also study the bi-valued instances, in which agents have at most two cost values on the chores. For three agents, we provide an algorithm for the computation of EFX allocations. For n>=4 agents, we present algorithms for the computation of partial EFX allocations with at most n-1 unallocated items; and (n-1)-approximation of EFX allocations.

cs.GT↗

arXiv2023

On the Existence of EFX (and Pareto-Optimal) Allocations for Binary Chores

We study the problem of allocating a group of indivisible chores among agents while each chore has a binary marginal. We focus on the fairness criteria of envy-freeness up to any item (EFX) and investigate the existence of EFX allocations. We show that when agents have additive binary cost functions, there exist EFX and Pareto-optimal (PO) allocations that can be computed in polynomial time. To the best of our knowledge, this is the first setting of a general number of agents that admits EFX and PO allocations, before which EFX and PO allocations have only been shown to exist for three bivalued agents. We further consider more general cost functions: cancelable and general monotone (both with binary marginal). We show that EFX allocations exist and can be computed for binary cancelable chores, but EFX is incompatible with PO. For general binary marginal functions, we propose an algorithm that computes (partial) envy-free (EF) allocations with at most $n-1$ unallocated items.

cs.GT↗

arXiv2023

One Quarter Each (on Average) Ensures Proportionality

We consider the problem of fair allocation of $m$ indivisible items to a group of $n$ agents with subsidy (money). Our work mainly focuses on the allocation of chores but most of our results extend to the allocation of goods as well. We consider the case when agents have (general) additive cost functions. Assuming that the maximum cost of an item to an agent can be compensated by one dollar, we show that a total of $n/4$ dollars of subsidy suffices to ensure a proportional allocation. Moreover, we show that $n/4$ is tight in the sense that there exists an instance with $n$ agents for which every proportional allocation requires a total subsidy of at least $n/4$. We also consider the weighted case and show that a total subsidy of $(n-1)/2$ suffices to ensure a weighted proportional allocation.

cs.GT↗

arXiv2023

Multi-agent Online Scheduling: MMS Allocations for Indivisible Items

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.

cs.GT↗

arXiv2023

Weighted EF1 Allocations for Indivisible Chores

We study how to fairly allocate a set of indivisible chores to a group of agents, where each agent $i$ has a non-negative weight $w_i$ that represents its obligation for undertaking the chores. We consider the fairness notion of weighted envy-freeness up to one item (WEF1) and propose an efficient picking sequence algorithm for computing WEF1 allocations. Our analysis is based on a natural and powerful continuous interpretation for the picking sequence algorithms in the weighted setting, which might be of independent interest. Using this interpretation, we establish the necessary and sufficient conditions under which picking sequence algorithms can guarantee other fairness notions in the weighted setting. We also study the existence of fair and efficient allocations and propose efficient algorithms for the computation of WEF1 and PO allocations for the bi-valued instances. Our result generalizes that of Garg et al. (AAAI 2022) and Ebadian et al. (AAMAS 2022) to the weighted setting. Our work also studies the price of fairness for WEF1, and the implications of WEF1 to other fairness notions.

cs.GT↗