Playing Games with Algorithms: Algorithmic Combinatorial Game Theory

Abstract

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in Combinatorial Game Theory, which analyzes ideal play in perfect-information games, and Constraint Logic, which provides a framework for showing hardness. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer.

DOI: 10.1007/3-540-44683-4_3

Extracted Key Phrases

17 Figures and Tables

Showing 1-10 of 125 references

Hartline and Ran Libeskind-Hadas. The computational complexity of motion planning

  • R Jeffrey
  • 2003

The Kung Fu Packing Crate Maze

  • Ste03 ] James W Stephens
  • 2003

The complexity of puzzles. Undergraduate thesis, Reed College

  • Brandon Mcphail
  • 2003

1 × n Konane: a summary of results

  • Alice Chan, Alice Tsai
  • 2002

Corral puzzles are NP-complete. Unpublished manuscript

  • Erich Friedman
  • 2002
01020'03'05'07'09'11'13'15'17
Citations per Year

167 Citations

Semantic Scholar estimates that this publication has received between 111 and 250 citations based on the available data.

See our FAQ for additional information.