TY - GEN
T1 - Polynomial-time approximation schemes for maximizing gross substitutes utility under budget constraints
AU - Shioura, Akiyoshi
PY - 2011
Y1 - 2011
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 -