On the exhaustive generation of k-convex polyominoes

نویسندگان

  • Stefano Brocchi
  • Giusi Castiglione
  • Paolo Massazza
چکیده

We present an algorithm to compute the degree of convexity of a convex polyomino P , defined as the smallest integer k such that any two cells of P can be joined by a path in P with at most k changes of direction. The algorithm is used to generate in amortized time O(1) all k-convex polyominoes of size n.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Generation and Enumeration of some Classes of Convex Polyominoes

ECO is a method for the recursive generation, and thereby also the enumeration of classes of combinatorial objects. It has already found successful application in recent literature both to the exhaustive generation and to the uniform random generation of various objects classified according to several parameters of interest, as well as to their enumeration. In this paper we extend this approach...

متن کامل

Reconstruction of 2-convex polyominoes

There are many notions of discrete convexity of polyominoes (namely hvconvex [1], Q-convex [2], L-convex polyominoes [5]) and each one has been deeply studied. One natural notion of convexity on the discrete plane leads to the definition of the class of hv-convex polyominoes, that is polyominoes with consecutive cells in rows and columns. In [1] and [6], it has been shown how to reconstruct in ...

متن کامل

Counting k-Convex Polyominoes

We compute an asymptotic estimate of a lower bound of the number of k-convex polyominoes of semiperimeter p. This approximation can be written as μ(k)p4p where μ(k) is a rational fraction of k which up to μ(k) is the asymptotics of convex polyominoes. A polyomino is a connected set of unit square cells drawn in the plane Z × Z [7]. The size of a polyomino is the number of its cells. A central p...

متن کامل

On the generation of convex polyominoes

We present a simple but efficient method for generating the set LPol(n) of L-convex polyominoes of size n. We show a bijection between LPol(n) and a suitable set of pairs of integer sequences. This lets us design a CAT (Constant Amortized Time) algorithm for generating LPol(n) using O( √ n) space.

متن کامل

Tiling the Plane with Permutations

A permutomino is a polyomino uniquely defined by a pair of permutations. Recently permutominoes, and in particular convex permutominoes have been studied by several authors concerning their analytical and bijective enumeration, tomographical reconstruction, and the algebraic characterization of the associated permutations [2, 3]. On the other side, Beauquier and Nivat [5] introduced and gave a ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Theor. Comput. Sci.

دوره 664  شماره 

صفحات  -

تاریخ انتشار 2017