Shannon switching game

Shannon switching game

The Shannon switching game is an abstract strategy game for two players, invented by "the father of information theory", Claude Shannon, and (at least in its common rectangular-grid form) independently invented by David Gale; it has also been known as "Gale", "Bridg-It", and "Bird Cage".

Rules

The game is played on a finite graph with two special nodes, "A" and "B". Each edge of the graph can be either colored or removed. The two players are called "Short" and "Cut", and alternate moves. On "Cut" 's turn, he deletes from the graph a non-colored edge of his choice. On "Short" 's turn, he colors any edge still in the graph. If "Cut" manages to turn the graph into one where "A" and "B" are no longer connected, he wins. If "Short" manages to create a colored path from "A" to "B", he wins.

There are also versions of the Shannon switching game played on a directed graph and an oriented matroid. A solution has been explicitly found for any such game using matroid theory, unlike a similar game Hex, which is PSPACE hard.

Winning algorithms

The game always terminates after a finite number of moves, and one of the two players has to win. Either "Short", "Cut", or the player moving first is guaranteed the existence of a winning strategy on any given graph. [cite journal|author=Stephen M. Chase |year=1972|title=An implemented graph algorithm for winning Shannon Switching Games | journal=Communications of the ACM | volume=15 | pages=253–256|doi=10.1145/361284.361293]

The "Short" and "Cut" games are a duality; that is, the game can be restated so that both players have the same goal: to secure a certain edge set with distinguished edge "e". "Short" tries to secure the edge set that with "e" makes up a circuit, while "Cut" tries to secure an edge set that with "e" makes up a cutset, the minimal set of edges that connect two subgraphs. [ [http://sky.fit.qut.edu.au/~maire/ALL/2004%20connectioin%20game%20book%20appendix%20%20maire-shannon.PDF Frederic Maire: "The Solution of Shannon Game"] , 2004]

References

External links

* [http://kryshen.pp.ru/games/graphg.html Graph Game] , a Java implementation of the Shannon switching game


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