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- W4225318447 abstract "We study the problem of fair and efficient allocation of a set of indivisible goods to agents with additive valuations using the popular fairness notions of envy-freeness up to one good (EF1) and equitability up to one good (EQ1) in conjunction with Pareto-optimality (PO). There exists a pseudo-polynomial time algorithm to compute an EF1+PO allocation, and a non-constructive proof of existence of allocations that are both EF1 and fractionally Pareto-optimal (fPO), which is a stronger notion than PO. We present a pseudo-polynomial time algorithm to compute an EF1+fPO allocation, thereby improving the earlier results. Our techniques also enable us to show that an EQ1+fPO allocation always exists when the values are positive, and that it can be computed in pseudo-polynomial time. We also consider the class of $k$-ary instances where $k$ is a constant, i.e., each agent has at most $k$ different values for the goods. We show that for such instances an EF1+fPO allocation can be computed in strongly polynomial time. When all values are positive, we show that an EQ1+fPO allocation for such instances can be computed in strongly polynomial time. Next, we consider instances where the number of agents is constant, and show that an EF1+PO (also EQ1+PO) allocation can be computed in polynomial time. These results significantly extend the polynomial-time computability beyond the known cases of binary or identical valuations. Further, we show that the problem of computing an EF1+PO allocation polynomial-time reduces to a problem in the complexity class PLS. We also design a polynomial-time algorithm that computes a Nash welfare maximizing allocation when there are constantly many agents with constant many different values for the goods." @default.
- W4225318447 created "2022-05-05" @default.
- W4225318447 creator A5049544227 @default.
- W4225318447 creator A5077432617 @default.
- W4225318447 date "2022-04-29" @default.
- W4225318447 modified "2023-09-27" @default.
- W4225318447 title "Computing Pareto-Optimal and Almost Envy-Free Allocations of Indivisible Goods" @default.
- W4225318447 doi "https://doi.org/10.48550/arxiv.2204.14229" @default.
- W4225318447 hasPublicationYear "2022" @default.
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