It is tough to be a plumber

  • Authors:

  • Daniel Král;Vladan Majerech;Jiří Sgall;Tomáš Tichý;Gerhard Woeginger

  • Affiliations:

  • Department of Applied Mathematics, Institute for Theoretical Computer Science (ITI), Charles University, Malostranské námesti 25, Prague 118 00, Czech Republic;Department of Theoretical Computer Science and Mathematical Logic (KTIML), Charles University, Malostranské námestí 25, Prague 118 00, Czech Republic;Dept. of Appl. Math., Inst. for Theor. Comp. Sci. (ITI), Charles Univ., Malostranské námesti 25, Prague and Math. Inst., AS CR, Zitná 25, CZ-11567 Praha 1 and Inst. for Comp. Sci., ...;Mathematical Institute, AS CR, Zitná 25, CZ-11567 Praha 1, Czech Republic and Institute for Computer Science, Prague, Czech Republic;Department of Mathematics, University of Twente, P.O. Box 217, AE 7500 Enschede, The Netherlands

  • Venue:
  • Theoretical Computer Science - Algorithmic combinatorial game theory
  • Year:
  • 2004

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Abstract

In the Linux computer game KPlumber, the objective is to rotate tiles in a raster of squares so as to complete a system of pipes. We give a complexity classification for the original game and various special cases of it that arise from restricting the set of six possible tiles.Most of the cases are NP-complete. One polynomially solvable case is settled by formulating it as a perfect matching problem; other polynomial cases are settled by simple sweepline techniques. Moreover, we show that all the unsettled cases are polynomial time equivalent.