On the bit complexity of minimum link paths: superquadratic algorithms for problems solvable in linear time

Abstract All of the linear-time algorithms that have been developed for minimum-link paths use the real RAM model of computation. If one considers bit complexity, however, merely representing a minimum-link path may require a superquadratic number of bits. This paper considers bounds on the number of links (segments) needed by limited-precision approximations of minimum-link paths: When vertices are restricted to ‘‘first-derived’’ points, the number of links can increase by a constant factor; when they are restricted to points of an N×N grid, the number of links can increase by Θ log N .

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