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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13766

Title: Route-Enabling Graph Orientation Problems
Authors: Ito, Takehiro
Miyamoto, Yuichiro
Ono, Hirotaka
Tamaki, Hisao
Uehara, Ryuhei
Keywords: approximation algorithm
dynamic programming
fully polynomial time approximation scheme
graph orientation
Issue Date: 2013-02
Publisher: Springer
Magazine name: Algorithmica
Volume: 65
Number: 2
Start page: 317
End page: 338
DOI: 10.1007/s00453-011-9589-z
Abstract: Given an undirected and edge-weighted graph G together with a set of ordered vertex-pairs, called st-pairs, we consider two 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. Note that these shortest directed paths for st-pairs are not necessarily edge-disjoint. 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 stpairs. 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.
Rights: This is the author-created version of Springer, Takehiro Ito, Yuichiro Miyamoto, Hirotaka Ono, Hisao Tamaki, and Ryuhei Uehara, Algorithmica, 65(2), 2013, 317-338. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s00453-011-9589-z
URI: http://hdl.handle.net/10119/13766
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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