CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions

Abstract

C ombinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is -complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster-especially in cases with structure. CABOB's search runs in linear space and has significantly better anytime performance than CPLEX.We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem-the run-time distribution does not have a heavy tail.

Enabling commodity environmental sensor networks using multi-attribute combinatorial marketplaces

“…In the approach here, adapted from combinatorial auctions in Management Science [29], the role of the marketplace M , is to efficiently match resource providers R with a set of bids for resource bundles B from resource consumers C. A bundle B is a combination of resources from a provider P such that B ⊆ R. A consumer C can bid for any subset of R. Assuming that B i is a set of bids b i = b 1 , b 2 , b 3 , ..., b n . A bid is a tuple B i = (B i , p i ) where B ⊆ R is a set of resources and P i ≥ 0 is a price.…”

Matrix Bidding in Combinatorial Auctions

“…Included in the latter, Lehmann et al (2006) discuss the complexity issues of winner determination, and Sandholm (2006) discusses winner-determination algorithms. Other prominent articles on winner-determination methods include Günlük et al (2005), and Sandholm et al (2005), based on XOR-of-OR and XOR logical languages of flat bids, respectively. Rothkopf et al (1998) provide a seminal paper in the study of combinatorial auctions, including some of the first detailed complexity results and the first discussion of "restricted-subset" combinatorial auctions for which winner determination is tractable.…”

“…Matrix bids provide a structured way to string together several k-of, exactly-k-of, and flat-bid sentence fragments to be read in a meaningful way after deleting many of the logical connectives. In §6, we will see that this allows us to quickly generate simulated auction data (with no logical connectives) which would have required exponentially long bid sentences in any of the flat-bid auction simulations commonly found in recent literature (for example Günlük et al, 2005;Leyton-Brown et al, 2002;Sandholm et al, 2005).…”

“…The type of data simulation used here is common in the combinatorial auction literature. Sandholm et al (2005) provide a prominent example, while Boutilier (2002) notes that the available benchmark data (i.e., the CATS test suite discussed by Leyton-Brown et al, 2002) may not always be beneficial for the testing of new language paradigms. In our case, we applied the algorithm of §4.1 to two-hundred of the CATS instances used for the computational experiments in Day and Raghavan (2007).…”

A Recombination-Based Tabu Search Algorithm for the Winner Determination Problem

“…Representative examples of exact methods include: Branchon-Items (BoI), Branch-on-Bids (BoB) [19], Combinatorial Auctions BoB (CABoB) [20], Combinatorial Auction Structural Search (CASS) [6] and Combinatorial Auctions Multi-unit Search (CAMUS) [15]. A dynamic programming approach is introduced in [17] while a linear programming method is investigated in [16].…”