Lower bounds on time complexity for some subgraph detection problems

Masanari Arai, Masafumi Yamashita, Tomio Hirata, Toshihide Ibaraki, Namio Honda

Research output: Contribution to journalArticle

Abstract

Nontrivial lower bounds of the time complexity are given for a class of problems on graphs. Specifically, given a complete graph with weighted edges, the problem of finding a subgraph satisfying a property π and having edge‐weights that sum exactly to unity is considered. An ω(n3 log n) lower bound is established under the algebraic decision tree model for a property π that satisfies the degree constraint and is closed with respect to isomorphism, where n is the number of vertices in an input graph. This result is a proper generalization of that of Nakayama et al. [8], in which the same lower bound was obtained for π that is hereditary on subgraphs and determined by components. Furthermore, an ω(n3) lower bound is shown for π = “clique” that does not satisfy the degree constraint and hence the above result can not be applied.

Original languageEnglish
Pages (from-to)95-102
Number of pages8
JournalSystems and Computers in Japan
Volume17
Issue number6
DOIs
Publication statusPublished - 1986

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Hardware and Architecture
  • Computational Theory and Mathematics

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