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

Osamu Maruyama, Satoru Miyano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

The graph inference from a walk for a class C of undirected edgecolored 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(nlog 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.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 1995 - 20th International Symposium, MFCS 1995, Proceedings
EditorsJiri Wiedermann, Petr Hajek
PublisherSpringer Verlag
Pages257-266
Number of pages10
ISBN (Print)3540602461, 9783540602460
DOIs
Publication statusPublished - 1995
Event20th International Symposium on Mathematical Foundations of Computer Science, MFCS 1995 - Prague, Czech Republic
Duration: Aug 28 1995Sep 1 1995

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume969
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other20th International Symposium on Mathematical Foundations of Computer Science, MFCS 1995
CountryCzech Republic
CityPrague
Period8/28/959/1/95

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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