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Graph inference from a walk for trees of bounded degree 3 is NP-complete

  • Osamu MaruyamaEmail author
  • Satoru Miyano
Contributed Papers Graphs in Models of Computations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

The graph inference from a walk for a class C of undirected edge-colored graphs is, given a string x of colors, finding the smallest graph G in C that allows a traverse of all edges in G whose sequence of edge-colors is x, called a walk for x. We prove that the graph inference from a walk for trees of bounded degree k is NP-complete for any k ⩾ 3, while the problem for trees without any degree bound constraint is known to be solvable in O(n) time, where n is the length of the string. Furthermore, the problem for a special class of trees of bounded degree 3, called (1,1)-caterpillars, is shown to be NP-complete. This contrast with the case that the problem for linear chains is known to be solvable in O(n log n) time since a (1,1)-caterpillar is obtained by attaching at most one hair of length one to each node of a linear chain. We also show the MAXSNP-hardness of these problems.

Keywords

Polynomial Time Small Tree Linear Chain Vertex Cover Polynomial Time Approximation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  1. 1.Department of Information SystemsKyushu University 39KasugaJapan
  2. 2.Research Institute of Fundamental Information ScienceKyushu University 33FukuokaJapan

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