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http://hdl.handle.net/10119/4920
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| Title: | Tree Spanners for Bipartite Graphs and Probe Interval Graphs |
| Authors: | Brandstadt, Andreas
Dragan, Feodor F.
Le, Hoang-Oanh
Le, Van Bang
Uehara, Ryuhei |
| Keywords: | Chordal bipartite graph
Interval bigraph
NP-completeness
Probe interval graph
Tree spanner |
| Issue Date: | 2007-01 |
| Publisher: | Springer |
| Magazine name: | Algorithmica |
| Volume: | 47 |
| Number: | 1 |
| Start page: | 27 |
| End page: | 51 |
| DOI: | 10.1007/s00453-006-1209-y |
| Abstract: | A tree t-spanner T in a graph G is a spanning tree of G such that the distance between every pair of vertices in T is at most t times their distance in G. The tree t-spanner problem asks whether a graph admits a tree t-spanner, given t. We first substantially strengthen the known results for bipartite graphs. We prove that the tree t-spanner problem is NP-complete even for chordal bipartite graphs for t ≥ 5, and every bipartite ATE–free graph has a tree 3-spanner, which can be found in linear time. The best known before results were NP-completeness for general bipartite graphs, and that every convex graph has a tree 3-spanner. We next focus on the tree t-spanner problem for probe interval graphs and related graph classes. The graph classes were introduced to deal with the physical mapping of DNA. From a graph theoretical point of view, the classes are natural generalizations of interval graphs. We show that these classes are tree 7-spanner admissible, and a tree 7-spanner can be constructed in O(m log n) time. |
| Rights: | This is the author-created version of Springer, Andreas Brandstadt, Feodor F. Dragan, Hoang-Oanh Le, Van Bang Le and Ryuhei Uehara, Algorithmica, 47(1), 2007, 27-51. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s00453-006-1209-y |
| URI: | http://hdl.handle.net/10119/4920 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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