论文信息 - APX-hardness of maximizing Nash social welfare with indivisible items

APX-hardness of maximizing Nash social welfare with indivisible items

We study the problem of allocating a set of indivisible items to agents with additive utilities to maximize the Nash social welfare. Cole and Gkatzelis recently proved that this problem admits a constant factor approximation. We complement their result by showing that this problem is APX-hard.

Euiwoong Lee | Euiwoong Lee

[1] Venkatesan Guruswami,et al. MaxMin allocation via degree lower-bounded arborescences , 2009, STOC '09.

[2] Jörg Rothe,et al. Computational complexity and approximability of social welfare optimization in multiagent resource allocation , 2012, Autonomous Agents and Multi-Agent Systems.

[3] Miroslav Chlebík,et al. Complexity of approximating bounded variants of optimization problems , 2006, Theor. Comput. Sci..

[4] Richard Cole,et al. Approximating the Nash Social Welfare with Indivisible Items , 2018, SIAM J. Comput..

[5] Nikhil R. Devanur,et al. Convex Program Duality, Fisher Markets, and Nash Social Welfare , 2016, EC.

[6] Mohit Singh,et al. Nash Social Welfare, Matrix Permanent, and Stable Polynomials , 2016, ITCS.