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On computing the degree of convexity of polyominoes


In this paper we present an algorithm which has as input a convex polyomino P and computes its degree of convexity, deļ¬ned as the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. The algorithm uses space O(m + n) to represent a polyomino P with n rows and m columns, and has time complexity O(min(m, rk)), where r is the number of corners of P. Moreover, the algorithm leads naturally to a decomposition of P into simpler polyominoes.