A Combinatorial Problem Which Is Complete in Polynomial Space

S. Even, R. E. Tarjan

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


This paper considers a generalization, called the Shannon switching game on vertices, of a familiar board game called Hex. It is shown that determining who wins such a game if each player plays perfectly is very hard; in fact, if this game problem is solvable in polynomial time, then any problem solvable in polynomial space is solvable in polynomial time. This result suggests that the theory of combinational games is difficult.

Original languageAmerican English
Pages (from-to)710-719
Number of pages10
JournalJournal of the ACM (JACM)
Issue number4
StatePublished - Oct 1 1976
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Hardware and Architecture
  • Artificial Intelligence

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