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On the exhaustive generation of k-convex polyominoes

  • Authors: Brocchi, S.; Castiglione, G.; Massazza, P.
  • Publication year: 2017
  • Type: Articolo in rivista (Articolo in rivista)
  • Key words: CAT algorithms; Convex polyominoes; Exhaustive generation; Theoretical Computer Science; Computer Science (all)
  • OA Link:


The degree of convexity of a convex polyomino P is 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. In this paper we present a simple algorithm for computing the degree of convexity of a convex polyomino and we show how it can be used to design an algorithm that generates, given an integer k, all k-convex polyominoes of area n in constant amortized time, using space O(n). Furthermore, by applying few changes, we are able to generate all convex polyominoes whose degree of convexity is exactly k.