Truthful unification framework for packing integer programs with choices

Abstract

One of the most interesting research directions within the field of algorithmic mechanism design revolves the study of hard combinatorial optimization problems. In this setting, many common algorithmic techniques cannot be utilized as they violate certain monotonicity properties that are imperative for truthfulness. Consequently, it seems of the essence to develop alternative methods, which can underlie truthful mechanisms. In particular, since many problems can be formulated as instances of integer linear programs, it seems that devising techniques that apply to integer linear programs is significantly important. In this paper, we focus our attention on packing integer programs with choices. Our main findings can be briefly summarized as follows: 1. We develop a framework, which can be used as a building block to approximately solve packing integer programs with choices. The framework is built upon a novel unification technique that approximately solves an instance of a packing integer program with choices, given algorithms that approximately solve sub-instances of it. The framework is deterministic and monotone, and hence can underlie truthful deterministic mechanisms. 2. We demonstrate the applicability of the framework by applying it to several NP-hard problems. In particular, we focus on the bandwidth allocation problem in tree networks, and the multiple knapsack problem on bipartite graphs. Notably, using the mentioned framework, we attain the first non-trivial approximation guarantees for these problems in a game theoretic setting. © 2008 Springer-Verlag.