### 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(n^{3} 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(n^{3}) lower bound is shown for π = “clique” that does not satisfy the degree constraint and hence the above result can not be applied.

Original language | English |
---|---|

Pages (from-to) | 95-102 |

Number of pages | 8 |

Journal | Systems and Computers in Japan |

Volume | 17 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1986 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Systems and Computers in Japan*,

*17*(6), 95-102. https://doi.org/10.1002/scj.4690170611

**Lower bounds on time complexity for some subgraph detection problems.** / Arai, Masanari; Yamashita, Masafumi; Hirata, Tomio; Ibaraki, Toshihide; Honda, Namio.

Research output: Contribution to journal › Article

*Systems and Computers in Japan*, vol. 17, no. 6, pp. 95-102. https://doi.org/10.1002/scj.4690170611

}

TY - JOUR

T1 - Lower bounds on time complexity for some subgraph detection problems

AU - Arai, Masanari

AU - Yamashita, Masafumi

AU - Hirata, Tomio

AU - Ibaraki, Toshihide

AU - Honda, Namio

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022737645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022737645&partnerID=8YFLogxK

U2 - 10.1002/scj.4690170611

DO - 10.1002/scj.4690170611

M3 - Article

AN - SCOPUS:0022737645

VL - 17

SP - 95

EP - 102

JO - Systems and Computers in Japan

JF - Systems and Computers in Japan

SN - 0882-1666

IS - 6

ER -