Skyline queries are important in many application domains. In this paper, we propose a novel structure Diagram, which given set of points, partitions the plane into regions, referred to as skyline polyominos. All query points same polyomino have results. Similar kth-order Voronoi diagram commonly used facilitate k nearest neighbor (kNN) queries, can be and other applications. However, it may co...

Spiral Galaxies is a pencil-and-paper puzzle played on grid of unit squares: given set points called centers , the goal to partition into polyominoes such that each polyomino contains exactly one center and 180 ∘ rotationally symmetric about its center. We show this NP-complete, ASP-complete, #P-complete even if (a) all solutions have rectangles for polyominoes; or (b) are required be just 1 × ...

A permutomino of size n is a polyomino determined by particular pairs (π1, π2) of permutations of length n, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n. In this paper we consider the class of convex permutominoes which are symmetric with respect to the diagonal x = y. We determine the number of these permutominoes according to the dimension and we characterize the class of permutations associated t...

In this talk I will highlight some results from a recent paper (arXiv:1208.0024) that was motived by a correspondence between bivincular permutation patterns and composition matrices. We study recurrent configurations of the sandpile model on the complete bipartite graph Km,n and show how they can be classified in terms of a class of polyominoes. A canonical toppling process on these recurrent ...

The paper investigates the layout optimisation problem for processor-array networks. If an appropriate shape geometry is selected for the processors, a specific interconnection network can be area-eficiently mapped on a VLSI/WSI chip to maximise the chip yield, operational reliability and circuit performance. A formal technique of cellular layout by polyomino tiles is proposed, with application...

This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice wins if she occupies a set of cells, the union of a subset of which is a translated or rotated copy of a previously agreed upon polyomino P (called an a...

Abstract During the last years, several card-based Zero-Knowledge Proof (ZKP) protocols for Nikoli’s puzzles have been designed. Although there are relatively simple ZKP a number of puzzles, such as Sudoku and Kakuro, some face difficulties in designing protocols. For example, Slitherlink requires novel elaborate techniques to construct protocol. In this study, we focus on three Nikoli puzzles:...

the aim of this study was to represent effective componentsin demand chain which help organizations attain high performance levelsthrough identification of these components and determining theirdegree of importance. the following questions were major ideas of thisstudy: what are the most effective components in demand chain? andhow are they effective on organizational performance? to this end,m...

We introduce the problem of polyomino Gray codes, which is the listing of all members of certain classes of polyominoes such 4 that successive polyominoes differ by some well-defined closeness condition (e.g., the movement of one cell). We discuss various 5 closeness conditions and provide several Gray codes for the class of column-convex polyominoes with a fixed number of cells 6 in each colum...

We propose a major index statistic on 01-fillings of moon polyominoes which, when specialized to certain shapes, reduces to the major index for permutations and set partitions. We consider the set F(M, s;A) of all 01-fillings of a moon polyomino M with given column sum s whose empty rows are A, and prove that this major index has the same distribution as the number of north-east chains, which a...