TY - GEN

T1 - Polynomial-time approximation schemes for maximizing gross substitutes utility under budget constraints

AU - Shioura, Akiyoshi

PY - 2011/9/20

Y1 - 2011/9/20

N2 - We consider the maximization of a gross substitutes utility function under budget constraints. This problem naturally arises in applications such as exchange economies in mathematical economics and combinatorial auctions in (algorithmic) game theory. We show that this problem admits a polynomial-time approximation scheme (PTAS). More generally, we present a PTAS for maximizing a discrete concave function called an M -concave function under budget constraints. Our PTAS is based on rounding an optimal solution of a continuous relaxation problem, which is shown to be solvable in polynomial time by the ellipsoid method. We also consider the maximization of the sum of two M -concave functions under a single budget constraint. This problem is a generalization of the budgeted max-weight matroid intersection problem to the one with a nonlinear objective function. We show that this problem also admits a PTAS.

AB - We consider the maximization of a gross substitutes utility function under budget constraints. This problem naturally arises in applications such as exchange economies in mathematical economics and combinatorial auctions in (algorithmic) game theory. We show that this problem admits a polynomial-time approximation scheme (PTAS). More generally, we present a PTAS for maximizing a discrete concave function called an M -concave function under budget constraints. Our PTAS is based on rounding an optimal solution of a continuous relaxation problem, which is shown to be solvable in polynomial time by the ellipsoid method. We also consider the maximization of the sum of two M -concave functions under a single budget constraint. This problem is a generalization of the budgeted max-weight matroid intersection problem to the one with a nonlinear objective function. We show that this problem also admits a PTAS.

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U2 - 10.1007/978-3-642-23719-5_1

DO - 10.1007/978-3-642-23719-5_1

M3 - Conference contribution

AN - SCOPUS:80052790261

SN - 9783642237188

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 12

BT - Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings

T2 - 19th Annual European Symposium on Algorithms, ESA 2011

Y2 - 5 September 2011 through 9 September 2011

ER -