Route-enabling graph orientation problems

Takehiro Ito, Yuichiro Miyamoto, Hirotaka Ono, Hisao Tamaki, Ryuhei Uehara

研究成果: Conference contribution

6 被引用数 (Scopus)


Given an undirected and edge-weighted graph G together with a set of ordered vertex-pairs, called st-pairs, we consider the problems of finding an orientation of all edges in G: min-sum orientation is to minimize the sum of the shortest directed distances between all st-pairs; and min-max orientation is to minimize the maximum shortest directed distance among all st-pairs. In this paper, we first show that both problems are strongly NP-hard for planar graphs even if all edge-weights are identical, and that both problems can be solved in polynomial time for cycles. We then consider the problems restricted to cacti, which form a graph class that contains trees and cycles but is a subclass of planar graphs. Then, min-sum orientation is solvable in polynomial time, whereas min-max orientation remains NP-hard even for two st-pairs. However, based on LP-relaxation, we present a polynomial-time 2-approximation algorithm for min-max orientation. Finally, we give a fully polynomial-time approximation scheme (FPTAS) for min-max orientation on cacti if the number of st-pairs is a fixed constant.

ホスト出版物のタイトルAlgorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
出版ステータスPublished - 2009
イベント20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States
継続期間: 2009 12 162009 12 18


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5878 LNCS


Other20th International Symposium on Algorithms and Computation, ISAAC 2009
国/地域United States
CityHonolulu, HI

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)


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