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Guarding Polyominoes Under k-Hop Visibility
AlgorithmicaWe study the Art Gallery Problem under k-hop visibility in polyominoes. In this visibility model, two unit squares of a polyomino can see each other if and only if the shortest path between the respective vertices in the dual graph of the polyomino has ...
Christiane Schmidt +2 more
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Medians and centres of polyominoes
Information Processing Letters, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yves Métivier, Nasser Saheb
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2016 IEEE Congress on Evolutionary Computation (CEC), 2016
A polyomino puzzle is a collection of polyominos that can be joined to make a simple shape. The game Ten-Yen was one of the first of these. It has ten polyomino pieces that could be used to make a 6×6 square in a variety of ways. In this study we define representations and fitness functions for generating polyomino puzzles as well as developing a ...
Daniel A. Ashlock, Lauren Taylor
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A polyomino puzzle is a collection of polyominos that can be joined to make a simple shape. The game Ten-Yen was one of the first of these. It has ten polyomino pieces that could be used to make a 6×6 square in a variety of ways. In this study we define representations and fitness functions for generating polyomino puzzles as well as developing a ...
Daniel A. Ashlock, Lauren Taylor
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A polyomino with no stochastic function
Combinatorica, 1984A polyomino P is defined to be a finite subset of the set S of unit squares with integer vertices in \(R^ 2\). A rectangle \(R^*\) of P is maximal if it is not properly contained in another rectangle of P. A function f from P to the non-negative reals is called a stochastic function if, for every maximal rectangle \(R^*\) of P, \(\sum_{s\in R^*}f(s)=1.\
Jeff Kahn 0001, Michael E. Saks
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Combinatorial properties of polyominoes
Combinatorica, 1981A finite set of cells in the infinite planar square grid is often called a polyomino. With each polyominoP, we may associate a hypergraph whose vertices are the cells ofP and whose edges are the maximal rectangles (in the standard position) contained inP.
Claude Berge 0001 +3 more
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Information Processing Letters, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Information Processing Letters, 1994
The perfect graph approach to study the combinatorial structure of visibility graphs in polyominos can be traced back to a paper of Berge et al., who made a survey of results and a collection of problems related to polyominos. In more recent works, Rajeev, Motwani et al.
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The perfect graph approach to study the combinatorial structure of visibility graphs in polyominos can be traced back to a paper of Berge et al., who made a survey of results and a collection of problems related to polyominos. In more recent works, Rajeev, Motwani et al.
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Smooth Column Convex Polyominoes
Discrete and Computational Geometry, 2022Toufik Mansour +2 more
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