A Faster Core Constraint Generation Algorithm for Combinatorial Auctions

8 years 1 months ago

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Computing prices in core-selecting combinatorial auctions is a computationally hard problem. Auctions with many bids can only be solved using a recently proposed core constraint generation (CCG) algorithm, which may still take days on hard instances. In this paper, we present a new algorithm that signiﬁcantly outperforms the current state of the art. Towards this end, we ﬁrst provide an alternative deﬁnition of the set of core constraints, where each constraint is weakly stronger, and prove that together these constraints deﬁne the identical polytope to the previous deﬁnition. Using these new theoretical insights we develop two new algorithmic techniques which generate additional constraints in each iteration of the CCG algorithm by 1) exploiting separability in allocative conﬂicts between participants in the auction, and 2) by leveraging non-optimal solutions. We show experimentally that our new algorithm leads to signiﬁcant speed-ups on a variety of large combinatorial...

Benedikt Bünz, Sven Seuken, Benjamin Lubin

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