TY - GEN

T1 - Finding a level ideal of a poset

AU - Kijima, Shuji

AU - Nemoto, Toshio

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-02882-3_32

DO - 10.1007/978-3-642-02882-3_32

M3 - Conference contribution

AN - SCOPUS:76249103766

SN - 3642028810

SN - 9783642028816

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 317

EP - 327

BT - Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings

T2 - 15th Annual International Conference on Computing and Combinatorics, COCOON 2009

Y2 - 13 July 2009 through 15 July 2009

ER -