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- W3202823408 abstract "We consider the fundamental problem of detecting/counting copies of a fixed pattern graph in a host graph. The recent progress on this problem has not included complete pattern graphs, i.e., cliques (and their complements, i.e., edge-free pattern graphs, in the induced setting). The fastest algorithms for the aforementioned patterns are based on a straightforward reduction to triangle detection/counting. We provide an alternative method of detection/counting copies of fixed size cliques based on a multi-dimensional matrix product. It is at least as time efficient as the triangle method in cases of $K_4$ and $K_5.$ The complexity of the multi-dimensional matrix product is of interest in its own rights. We provide also another alternative method for detection/counting $K_r$ copies, again time efficient for $rin { 4, 5 }$." @default.
- W3202823408 created "2021-10-11" @default.
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- W3202823408 date "2022-01-01" @default.
- W3202823408 modified "2023-09-26" @default.
- W3202823408 title "Breaking the Hegemony of the Triangle Method in Clique Detection" @default.
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- W3202823408 doi "https://doi.org/10.2139/ssrn.4016393" @default.
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