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On the Problem of Deciding If a Polyomino Tiles the Plane by Translation
, 2006
"... The words that tile the plane by translation are characterized by the BeauquierNivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudosquare polyominoes, improving the previous quadrat ..."
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Cited by 1 (0 self)
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The words that tile the plane by translation are characterized by the BeauquierNivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudosquare polyominoes, improving the previous
On the Problem of Deciding If a Polyomino Tiles the Plane by Translation⋆
"... Abstract. The words that tile the plane by translation are characterized by the BeauquierNivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudosquare polyominoes, improving the previo ..."
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Abstract. The words that tile the plane by translation are characterized by the BeauquierNivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudosquare polyominoes, improving
On the Problem of Deciding If a Polyomino Tiles the Plane by Translation⋆
"... Abstract. The words that tile the plane by translation are characterized by the BeauquierNivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudosquare polyominoes, improving the previo ..."
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Abstract. The words that tile the plane by translation are characterized by the BeauquierNivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudosquare polyominoes, improving
An Algorithm for Deciding If a Polyomino Tiles the Plane by Translations
"... We explain a fast algorithm to decide if a polyomino tiles the plane by translations. More precisely, if the polyomino has a boundary word of length n then the algorithm decides if the polyomino tiles the plane by translations in O(n²) operations (rather than O(n^4) operations for the naive ..."
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Cited by 13 (2 self)
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We explain a fast algorithm to decide if a polyomino tiles the plane by translations. More precisely, if the polyomino has a boundary word of length n then the algorithm decides if the polyomino tiles the plane by translations in O(n²) operations (rather than O(n^4) operations
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 448 (3 self)
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for speedingup the offline rendering of complex scenes. Unfortunately, generating these levels of detail is a timeconsuming task usually left to a human modeler. This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a retiling of a
An Optimal Algorithm for Tiling the Plane with a Translated Polyomino
"... We give a O(n)time algorithm for determining whether translations of a polyomino with n edges can tile the plane. The algorithm is also a O(n)time algorithm for enumerating all such tilings that are also regular, and we prove that at most Θ(n) such tilings exist. 1 ..."
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We give a O(n)time algorithm for determining whether translations of a polyomino with n edges can tile the plane. The algorithm is also a O(n)time algorithm for enumerating all such tilings that are also regular, and we prove that at most Θ(n) such tilings exist. 1
Tiling the Plane with a Fixed Number of polyominoes
, 2008
"... Deciding whether a finite set of polyominoes tiles the plane is undecidable by reduction from the Domino problem. In this paper, we prove that the problem remains undecidable if the set of instances is restricted to sets of 5 polyominoes. In the case of tiling by translations only, we prove that the ..."
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Cited by 3 (0 self)
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Deciding whether a finite set of polyominoes tiles the plane is undecidable by reduction from the Domino problem. In this paper, we prove that the problem remains undecidable if the set of instances is restricted to sets of 5 polyominoes. In the case of tiling by translations only, we prove
POLYOMINO CONVOLUTIONS AND TILING PROBLEMS
, 2000
"... Abstract. We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and show that the criterion detects some cases that are ..."
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Abstract. We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and show that the criterion detects some cases
Cognitive load during problem solving: effects on learning
 COGNITIVE SCIENCE
, 1988
"... Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problemsolving skill. Evidence that conventional problemsolving activity is not effective in schema acquisition is also accumulating. It is suggested t ..."
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Cited by 603 (13 self)
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that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes required by the two activities overlap insufficiently, and that conventional problem solving in the form of meansends analysis requires a relatively large amount of cognitive processing
Scale and performance in a distributed file system
 ACM Transactions on Computer Systems
, 1988
"... The Andrew File System is a locationtransparent distributed tile system that will eventually span more than 5000 workstations at Carnegie Mellon University. Large scale affects performance and complicates system operation. In this paper we present observations of a prototype implementation, motivat ..."
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Cited by 937 (47 self)
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The Andrew File System is a locationtransparent distributed tile system that will eventually span more than 5000 workstations at Carnegie Mellon University. Large scale affects performance and complicates system operation. In this paper we present observations of a prototype implementation
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