Finding a level ideal of a poset

Shuji Kijima, Toshio Nemoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

This paper is concerned with finding a level ideal (LI) of a partially ordered set (poset): given a finite poset P, a level of each element p ∈ P is defined as the number of ideals which do not include p, then the problem is to find an ideal consisting of elements whose levels are less than a given integer i. We call the ideal as the i-th LI. The concept of the level ideal is naturally derived from the generalized median stable matching, that is a fair stable marriage introduced by Teo and Sethuraman (1998). Cheng (2008) showed that finding the i-th LI is #P-hard when i=Θ(N), where N is the total number of ideals of P. This paper shows that finding the i-th LI is #P-hard even if i=Θ(N1/c) where c≥1 is an arbitrary constant. Meanwhile, we give a polynomial time exact algorithm when i=O((logN)c′) where c′ is an arbitrary positive constant. We also devise two randomized approximation schemes using an oracle of almost uniform sampler for ideals of a poset.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings
Pages317-327
Number of pages11
DOIs
Publication statusPublished - Dec 1 2009
Externally publishedYes
Event15th Annual International Conference on Computing and Combinatorics, COCOON 2009 - Niagara Falls, NY, United States
Duration: Jul 13 2009Jul 15 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5609 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th Annual International Conference on Computing and Combinatorics, COCOON 2009
CountryUnited States
CityNiagara Falls, NY
Period7/13/097/15/09

Fingerprint

Partially Ordered Set
Polynomials
Stable Marriage
Stable Matching
Arbitrary
Exact Algorithms
Approximation Scheme
Polynomial-time Algorithm
Integer

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kijima, S., & Nemoto, T. (2009). Finding a level ideal of a poset. In Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings (pp. 317-327). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5609 LNCS). https://doi.org/10.1007/978-3-642-02882-3_32

Finding a level ideal of a poset. / Kijima, Shuji; Nemoto, Toshio.

Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings. 2009. p. 317-327 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5609 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kijima, S & Nemoto, T 2009, Finding a level ideal of a poset. in Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5609 LNCS, pp. 317-327, 15th Annual International Conference on Computing and Combinatorics, COCOON 2009, Niagara Falls, NY, United States, 7/13/09. https://doi.org/10.1007/978-3-642-02882-3_32
Kijima S, Nemoto T. Finding a level ideal of a poset. In Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings. 2009. p. 317-327. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-02882-3_32
Kijima, Shuji ; Nemoto, Toshio. / Finding a level ideal of a poset. Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings. 2009. pp. 317-327 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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