Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficiently computing Groebner bases of ideals of points   We present an algorithm for computing Groebner bases of vanishing ideals of
points that is optimized for the case when the number of points in the
associated variety is less than the number of indeterminates. The algorithm
first identifies a set of essential variables, which reduces the time
complexity with respect to the number of indeterminates, and then uses PLU
decompositions to reduce the time complexity with respect to the number of
points. This gives a theoretical upper bound for its time complexity that is an
order of magnitude lower than the known one for the standard Buchberger-Moeller
algorithm if the number of indeterminates is much larger than the number of
points. Comparison of implementations of our algorithm and the standard
Buchberger-Moeller algorithm in Macaulay 2 confirm the theoretically predicted
speedup. This work is motivated by recent applications of Groebner bases to the
problem of network reconstruction in molecular biology.

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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci