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http://hdl.handle.net/10119/11474
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| Title: | Reconstruction Algorithms for Permutation Graphs and Distance-Hereditary Graphs |
| Authors: | Kiyomi, Masashi
Saitoh, Toshiki
Uehara, Ryuhei |
| Keywords: | the graph reconstruction conjecture
permutation graphs
polynomial time algorithm |
| Issue Date: | 2013-03-01 |
| Publisher: | 電子情報通信学会 |
| Magazine name: | IEICE TRANSACTIONS on Information and Systems |
| Volume: | E96-D |
| Number: | 3 |
| Start page: | 426 |
| End page: | 432 |
| Abstract: | PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n^8) time algorithm for PREIMAGE CONSTRUCTION on permutation graphs and an O(n^4(n+m)) time algorithm for PREIMAGE CONSTRUCTION on distance-hereditary graphs, where n is the number of graphs in the input, and m is the number of edges in a preimage. Since each graph of the input has n-1 vertices and O(n^2) edges, the input size is O(n^3) (, or O(nm)). There are polynomial time isomorphism algorithms for permutation graphs and distance-hereditary graphs. However the number of permutation (distance-hereditary) graphs obtained by adding a vertex to a permutation (distance-hereditary) graph is generally exponentially large. Thus exhaustive checking of these graphs does not achieve any polynomial time algorithm. Therefore reducing the number of preimage candidates is the key point. |
| Rights: | Copyright (C)2013 IEICE. Masashi Kiyomi, Toshiki Saitoh, and Ryuhei Uehara, IEICE TRANSACTIONS on Information and Systems, E96-D(3), 2013, 426-432. http://www.ieice.org/jpn/trans_online/ |
| URI: | http://hdl.handle.net/10119/11474 |
| Material Type: | publisher |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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| 19111.pdf | | 540Kb | Adobe PDF | View/Open |
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