Edge-Matching Problems with Rotations

Martin Ebbesen, Paul Fischer, Carsten Witt

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


    Edge-matching problems, also called puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem has gained interest recently with the (now terminated) Eternity II puzzle, and new complexity results. In this paper we consider a number of settings which differ in size of the puzzles and the manipulations allowed on the pieces. We investigate the effect of allowing rotations of the pieces on the complexity of the problem, an aspect that is only marginally treated so far. We show that some problems have polynomial time algorithms while others are NP-complete. Especially we show that allowing rotations in one-row puzzles makes the problem NP-hard. We moreover show that many commonly considered puzzles can be emulated by simple puzzles with quadratic pieces, so that one can restrict oneself to investigating those.
    Original languageEnglish
    Title of host publicationFundamentals of Computation Theory : 18th International Symposium, FCT 2011 Oslo, Norway, August 22-25, 2011 Proceedings
    Publication date2011
    ISBN (Print)978-3-642-22952-7
    ISBN (Electronic)978-3-642-22953-4
    Publication statusPublished - 2011
    EventInternational Symposium on Fundamentals of Computation Theory - Oslo, Norway
    Duration: 1 Jan 2011 → …
    Conference number: 18


    ConferenceInternational Symposium on Fundamentals of Computation Theory
    CityOslo, Norway
    Period01/01/2011 → …
    SeriesLecture Notes in Computer Science


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