TY - GEN

T1 - Route-enabling graph orientation problems

AU - Ito, Takehiro

AU - Miyamoto, Yuichiro

AU - Ono, Hirotaka

AU - Tamaki, Hisao

AU - Uehara, Ryuhei

N1 - Funding Information:
This work is partially supported by Grant-in-Aid for Scientific Research: 20650002, 20700003 and 21680001.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-10631-6_42

DO - 10.1007/978-3-642-10631-6_42

M3 - Conference contribution

AN - SCOPUS:75649091880

SN - 3642106307

SN - 9783642106309

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

SP - 403

EP - 412

BT - Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings

T2 - 20th International Symposium on Algorithms and Computation, ISAAC 2009

Y2 - 16 December 2009 through 18 December 2009

ER -