Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Opportunity Cost Algorithms for Combinatorial Auctions   Two general algorithms based on opportunity costs are given for approximating
a revenue-maximizing set of bids an auctioneer should accept, in a
combinatorial auction in which each bidder offers a price for some subset of
the available goods and the auctioneer can only accept non-intersecting bids.
Since this problem is difficult even to approximate in general, the algorithms
are most useful when the bids are restricted to be connected node subsets of an
underlying object graph that represents which objects are relevant to each
other. The approximation ratios of the algorithms depend on structural
properties of this graph and are small constants for many interesting families
of object graphs. The running times of the algorithms are linear in the size of
the bid graph, which describes the conflicts between bids. Extensions of the
algorithms allow for efficient processing of additional constraints, such as
budget constraints that associate bids with particular bidders and limit how
many bids from a particular bidder can be accepted.

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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: math
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph