Tractable Combinatorial Auctions Via Graph Matching

Combinatorial auctions play a key role in distributed AI as a mechanism for efficiently allocating resources or tasks, both for cooperative and competitive scenarios. The complexity of the general problem has lead to interest in finding efficient algorithms for useful instances. Tennenholtz introduced an approach which finds polynomial solutions for certain classes of combinatorial auctions by a reduction to graph matching problems. This paper looks at the possibilities and limits of this graph-matching approach. We extend the set of known tractable combinatorial auctions identified by Tennenholtz to accommodate subadditive symmetric bids over bundles of unlimited size, certain restricted cases of asymmetric discounts over bundles, and certain restricted cases of superadditive bids. We provide results on the ultimate limits of the approach, identifying classes of auctions which cannot be reduced to 2D graph matching, and classes which are NP-equivalent. We provide complexity results for the solution of the identified classes of tractable auctions, using the current best available graph matching algorithms. c ©2007 AI Access Foundation. All rights reserved.