Browsing by Subject "Polyominoes"

Now showing 1 - 2 of 2

Open Access
A decomposition of column-convex polyominoes and two vertex statistics
(Springer, 2022-04-27) Cakić, N.; Mansour, T.; Yıldırım, Gökhan
We introduce a decomposition method for column-convex polyominoes and enumerate them in terms of two statistics: the number of internal vertices and the number of corners in the boundary. We first find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of interior vertices. In particular, we show that the average number of interior vertices over all column-convex polyominoes of perimeter 2n is asymptotic to αon3 / 2 where αo≈ 0.57895563 …. We also find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of corners in the boundary. In particular, we show that the average number of corners over all column-convex polyominoes of perimeter 2n is asymptotic to α1n where α1≈ 1.17157287 …. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Open Access
Disconnected graph layout and the polyomino packing approach
(Springer, Berlin, Heidelberg, 2002) Freivalds, K.; Doğrusöz, Uğur; Kikusts, P.
We review existing algorithms and present a new approach for layout of disconnected graphs. The new approach is based on polyomino representation of components as opposed to rectangles. The parameters of our algorithm and their influence on the drawings produced as well as a variation of the algorithm for multiple pages are discussed. We also analyze our algorithm both theoretically and experimentally and compare it with the existing ones. The new approach produces much more compact and uniform drawings than previous methods. © Springer-Verlag Berlin Heidelberg 2002.