Presentation	2011-06-30 On the Constant Depth Circuit Complexity of Subgraph Isomorphism on Random Graphs Koutarou NAKAGAWA,
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Abstract(in English)	The AC^0 circuit complexity of k-clique on random graphs is already known. Rossman established the lower bound n^<ω(k/4)> in 2008, and Amano establishd the upper bound n^ in 2009. But complexity of subgraph isomorphism is still unknown. These results, for compute complexity of k-clique problem, are can applcate to subgraph isomorphism. So by the new function c(H) and c(H), we can represent the Rossman's result is n^ lower bound and Amano's result is n^ upper bound of subgraph isomorphism. But c(H) and c(H) are not so simple. In this paper, we prove that these bounds are not tight, namely, gap between c(H) and c(H) is large by showing that a family of graph that elements have constant c(H) and proportion to the size tildac(H). This means that, the complexity of this problem is still unknown, And c(H) or c(H) to be room for implovement.
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Paper #	COMP2011-20
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Conference Information
Committee	COMP
Conference Date	2011/6/23(1days)
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Registration To	Theoretical Foundations of Computing (COMP)
Language	ENG
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Title (in English)	On the Constant Depth Circuit Complexity of Subgraph Isomorphism on Random Graphs
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1st Author's Name	Koutarou NAKAGAWA
1st Author's Affiliation	Department of Mathematical and Computing Sciences, Graduate School of Information Science and Engineering, Tokyo Institute of Technology()
Date	2011-06-30
Paper #	COMP2011-20
Volume (vol)	vol.111
Number (no)	113
Page	pp.pp.-
#Pages	5
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