We propose a new approach to understanding the algorithm-specific empirical hardness of NP-Hard optimization problems. In this work we focus on the empirical hardness of the winner determination problem—an optimization problem arising in combinatorial auctions—when solved by ILOG’s CPLEX software. We consider nine widely-used problem distributions and sample randomly from a continuum of paramet...

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winn...

We consider the problem of winner determination under Chamberlin–Courant’s multiwinner voting rule with approval utilities. This problem is equivalent to the well-known NP-complete MaxCover problem and, so, the best polynomial-time approximation algorithm for it has approximation ratio 1−1/e. We show exponential-time/FPT approximation algorithms that, on one hand, achieve arbitrarily good appro...

To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, repeatedly choosing winner that we delete rank at the top, loser bottom. The latter method captures frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, Baldwin. In an experimental analysis,...

This thesis studies the computational complexity of different problems from three areas of computational social choice. The first one is voting, and especially the problem of determining whether a distinguished candidate can be a winner in an election with some kind of incomplete information. The second setting is in the broader sense related to the problem of determining winners. Here the comp...

A combinatorial auction is an auction that permits bidders to bid on bundles of goods rather than just a single item. Unfortunately, winner determination for combinatorial auctions is known to be NPhard. In this paper, we propose a distributed algorithm to compute optimal solutions to this problem. The algorithm uses nagging, a technique for parallelizing search in heterogeneous distributed com...

In a combinational auction in which bidders can bid on any combination of goods, bid data can be of exponential size. We describe an innovative new combinatorial auction format in which bidders submit “matrix bids”. The advantage of this approach is that it provides bidders a mechanism to compactly express bids on every possible bundle. We describe many different types of preferences that can b...

We present a cryptographic protocol for conducting efficient, provably-correct and secrecy-preserving combinatorial clock-proxy auctions. The “clock phase” functions as a trusted auction despite price discovery: bidders submit encrypted bids, and prove for themselves that they meet activity rules, and can compute total demand and thus verify price increases without revealing any information abo...

In the Possible Winner problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the Possible Winner problem, with number of candida...