Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Triangles under Updates in Worst-Case Optimal Time   We consider the problem of incrementally maintaining the triangle count query
under single-tuple updates to the input relations. We introduce an approach
that exhibits a space-time tradeoff such that the space-time product is
quadratic in the size of the input database and the update time can be as low
as the square root of this size. This lowest update time is worst-case optimal
conditioned on the Online Matrix-Vector Multiplication conjecture. The
classical and factorized incremental view maintenance approaches are recovered
as special cases of our approach within the space-time tradeoff. In particular,
they require linear-time update maintenance, which is suboptimal. Our approach
also recovers the worst-case optimal time complexity for computing the triangle
count in the non-incremental setting.

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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas