Computing the exact distribution function of the stochastic longest path length in a dag

Ei Ando, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita

研究成果: 著書/レポートタイプへの貢献会議での発言

2 引用 (Scopus)

抜粋

Consider the longest path problem for directed acyclic graphs (DAGs), where a mutually independent random variable is associated with each of the edges as its edge length. Given a DAG G and any distributions that the random variables obey, let F MAX(x) be the distribution function of the longest path length.We first represent F MAX(x) by a repeated integral that involves n-1 integrals, where n is the order of G. We next present an algorithm to symbolically execute the repeated integral, provided that the random variables obey the standard exponential distribution. Although there can be ω(2 n) paths in G, its running time is bounded by a polynomial in n, provided that k, the cardinality of the maximum anti-chain of the incidence graph of G, is bounded by a constant. We finally propose an algorithm that takes x and e > 0 as inputs and approximates the value of repeated integral of x, assuming that the edge length distributions satisfy the following three natural conditions: (1) The length of each edge (vi, vj) e E is non-negative, (2) the Taylor series of its distribution function Fij (x) converges to Fij (x), and (3) there is a constant σ that satisfies σ p ≤ (d/dx) p Fij(x) for any non-negative integer p. It runs in polynomial time in n, and its error is bounded by e, when x, e, σ and k can be regarded as constants.

元の言語英語
ホスト出版物のタイトルTheory and Applications of Models of Computation - 6th Annual Conference, TAMC 2009, Proceedings
ページ98-107
ページ数10
DOI
出版物ステータス出版済み - 7 16 2009
イベント6th Annual Conference on Theory and Applications of Models of Computation, TAMC 2009 - Changsha, 中国
継続期間: 5 18 20095 22 2009

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5532 LNCS
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

その他

その他6th Annual Conference on Theory and Applications of Models of Computation, TAMC 2009
中国
Changsha
期間5/18/095/22/09

    フィンガープリント

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

これを引用

Ando, E., Ono, H., Sadakane, K., & Yamashita, M. (2009). Computing the exact distribution function of the stochastic longest path length in a dag. : Theory and Applications of Models of Computation - 6th Annual Conference, TAMC 2009, Proceedings (pp. 98-107). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 5532 LNCS). https://doi.org/10.1007/978-3-642-02017-9_13