Taming The Knight'S Tour: Minimizing Turns And Crossings

Juan Jose Besa,Timothy Johnson,Nil Mamano,Martha C. Osegueda

GRAPH DRAWING AND NETWORK VISUALIZATION, GD 2018（2018）

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摘要

•There are knight's tours in n×n boards with less than 9.25n turns and 12n crossings.•Any knight's tour in an n×n board has over 5.99n turns and 4n crossings.•Using a 2×2 formation of parallel knight moves helps reduce both turns and crossings.•A new knight's tour algorithm minimizes turns and crossings simultaneously.•Our new knight's tour algorithm can be generalized to 3D boards and similar pieces.

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关键词

Graph drawing,Chess,Hamiltonian cycle,Approximation algorithms

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