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http://hdl.handle.net/10119/13766
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| Title: | Route-Enabling Graph Orientation Problems |
| Authors: | Ito, Takehiro
Miyamoto, Yuichiro
Ono, Hirotaka
Tamaki, Hisao
Uehara, Ryuhei |
| Keywords: | approximation algorithm
reachability
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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