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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
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
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
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
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
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2210 (37 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available
Instancebased learning algorithms
 Machine Learning
, 1991
"... Abstract. Storing and using specific instances improves the performance of several supervised learning algorithms. These include algorithms that learn decision trees, classification rules, and distributed networks. However, no investigation has analyzed algorithms that use only specific instances to ..."
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Cited by 1359 (18 self)
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to solve incremental learning tasks. In this paper, we describe a framework and methodology, called instancebased learning, that generates classification predictions using only specific instances. Instancebased learning algorithms do not maintain a set of abstractions derived from specific instances
The Omega Test: a fast and practical integer programming algorithm for dependence analysis
 Communications of the ACM
, 1992
"... The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method ..."
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Cited by 521 (15 self)
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The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method
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