Route-Enabling Graph Orientation Problems

  • Authors:

  • Takehiro Ito;Yuichiro Miyamoto;Hirotaka Ono;Hisao Tamaki;Ryuhei Uehara

  • Affiliations:

  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan 980-8579;Faculty of Science and Technology, Sophia University, Tokyo, Japan 102-8554;Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan 819-0395;School of Science and Technology, Meiji University, Kanagawa, Japan 214-8571;School of Information Science, JAIST, Ishikawa, Japan 923-1292

  • Venue:
  • ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

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.