Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Substitute Valuations: Generation and Structure   Substitute valuations (in some contexts called gross substitute valuations)
are prominent in combinatorial auction theory. An algorithm is given in this
paper for generating a substitute valuation through Monte Carlo simulation. In
addition, the geometry of the set of all substitute valuations for a fixed
number of goods K is investigated. The set consists of a union of polyhedrons,
and the maximal polyhedrons are identified for K=4. It is shown that the
maximum dimension of the maximal polyhedrons increases with K nearly as fast as
two to the power K. Consequently, under broad conditions, if a combinatorial
algorithm can present an arbitrary substitute valuation given a list of input
numbers, the list must grow nearly as fast as two to the power K.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc