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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/11474

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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