Paper by Erik D. Demaine

Reference:

Oswin Aichholzer, David Bremner, Erik D. Demaine, Ferran Hurtado, Evangelos Kranakis, Hannes Krasser, Suneeta Ramaswami, Saurabh Sethia, and Jorge Urrutia, “Games on Triangulations”, Theoretical Computer Science, volume 343, number 1–2, October 2005, pages 42–71. Special issue “Game Theory Meets Theoretical Computer Science”.

BibTeX

@Article{TriangulationGames_TCS,
  AUTHOR        = {Oswin Aichholzer and David Bremner and Erik D. Demaine and
                   Ferran Hurtado and Evangelos Kranakis and Hannes Krasser and
                   Suneeta Ramaswami and Saurabh Sethia and Jorge Urrutia},
  TITLE         = {Games on Triangulations},
  JOURNAL       = {Theoretical Computer Science},
  journalurl    = {https://www.journals.elsevier.com/theoretical-computer-science},
  VOLUME        = 343,
  NUMBER        = {1--2},
  MONTH         = {October},
  YEAR          = 2005,
  PAGES         = {42--71},
  NOTE          = {Special issue
                   ``Game Theory Meets Theoretical Computer Science''.},

  papers        = {TriangulationGames_JCDCG2002; TriangulationGames_EuroCG2003},
  length        = {32 pages},
  replaces      = {TriangulationGames_JCDCG2002; TriangulationGames_EuroCG2003},
  doi           = {https://dx.doi.org/10.1016/J.TCS.2005.05.007},
  dblp          = {https://dblp.org/rec/journals/tcs/AichholzerBDHKKRSU05},
  comments      = {This paper is also available from
                   <A HREF="http://dx.doi.org/10.1016/j.tcs.2005.05.007">ScienceDirect</A>.},
}

Abstract:

We analyze several perfect-information combinatorial games played on planar triangulations. We introduce three broad categories of such games—constructing, transforming, and marking triangulations—and several specific games within each category. In various situations of each game, we develop polynomial-time algorithms to determine who wins a given game position under optimal play, and to find a winning strategy. Along the way, we show connections to existing combinatorial games such as Kayles and Nimstring (a variation on Dots-and-Boxes).

Comments:

This paper is also available from ScienceDirect.

Length:

The paper is 32 pages.

Availability:

The paper is available in PostScript (1636k), gzipped PostScript (625k), and PDF (293k).

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Related papers:

TriangulationGames_JCDCG2002 (Playing with Triangulations)

TriangulationGames_EuroCG2003 (Geometric Games on Triangulations)