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ON COMPUTING THE FREQUENCIES OF INDUCED SUBHYPERGRAPHS

机译:关于归纳超图的频率计算

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摘要

Let F be an r-uniform hypergraph with / vertices, where / > r ≥3. In [Inform. Process. Lett., 99 (2006), pp. 130-134], Yuster posed the problem of whether there exists an algorithm which, for a given r-uniform hypergraph H with n vertices, computes the number of induced copies of F in H in time o(n~f). The analogous question for graphs (r = 2) was known to hold from an O{n~f-ε) time algorithm of Nesetril and Poljak [Comment. Math. Univ. Carolin., 26 (1985), pp. 415-419] (for a constant ε = ε_f > 0 which is independent of n). Here, we present an algorithm for this problem, when r ≥ 3, with running time O(n~f / log_2~n).
机译:令F为具有/顶点的r一致超图,其中/> r≥3。在[通知。处理。 [Lett。,99(2006),pp。130-134],Yuster提出了以下问题:对于给定的具有n个顶点的r均匀超图H,是否存在一种算法,可以计算H中H的F的诱导副本数。时间o(n〜f)。根据Nesetril和Poljak的O(n〜f-ε)时间算法,已知图的类似问题(r = 2)。数学。大学Carolin。,26(1985),第415-419页](对于常数ε=ε_f> 0,它与n无关)。在这里,我们提出一个针对该问题的算法,当r≥3时,运行时间为O(n〜f / log_2〜n)。

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