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Approximating the maximum independent set and minimum vertex coloring on box graphs
, 2007
"... A box graph is the intersection graph of a finite set of orthogonal rectangles in the plane. The problem of whether or not the maximum independent set problem (MIS for short) for box graphs can be approximated within a substantially sublogarithmic factor in polynomial time has been open for severa ..."
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(log n) factor from the size of its maximum clique and provide an O(log n) approximation algorithm for minimum vertex coloring of such a box graph. More generally, we can show that the chromatic number of the intersection graph of n ddimensional orthogonal rectangles is within an O(log dâˆ’1 n) factor
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and c ..."
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Cited by 774 (20 self)
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We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
The Vertex Coloring Algorithm
"... We present a new polynomialtime algorithm for finding proper mcolorings of the vertices of a graph. We prove that every graph with n vertices and maximum vertex degree must have chromatic number (G) less than or equal to +1 and that the algorithm will always find a proper mcoloring of the vertic ..."
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examples of famous graphs, including a proper fourcoloring of the map of India and two large Mycielski benchmark graphs with hidden minimum vertex colorings. We implement the algorithm in C++ and provide a demonstration program for
Retiming Synchronous Circuitry
 ALGORITHMICA
, 1991
"... This paper describes a circuit transformation called retiming in which registers are added at some points in a circuit and removed from others in such a way that the functional behavior of the circuit as a whole is preserved. We show that retiming can be used to transform a given synchronous circui ..."
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Cited by 376 (3 self)
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circuit into a more efficient circuit under a variety of different cost criteria. We model a circuit as a graph in which the vertex set Visa collection of combinational logic elements and the edge set E is the set of interconnections, each of which may pass through zero or more registers. We give an 0(V
Approximation Algorithms for Connected Dominating Sets
 Algorithmica
, 1996
"... The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, whe ..."
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Cited by 366 (9 self)
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The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size
Geometry Compression
"... This paper introduces the concept of Geometry Compression, allowing 3D triangle data to be represented with a factor of 6 to 10 times fewer bits than conventional techniques, with only slight losses in object quality. The technique is amenable to rapid decompression in both software and hardware imp ..."
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Cited by 350 (0 self)
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implementations; if 3D rendering hardware contains a geometry decompression unit, application geometry can be stored in memory in compressed format. Geometry is first represented as a generalized triangle mesh, a data structure that allows each instance of a vertex in a linear stream to specify an average of two
A Data Structure for Dynamic Trees
, 1983
"... A data structure is proposed to maintain a collection of vertexdisjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) ti ..."
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Cited by 347 (21 self)
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A data structure is proposed to maintain a collection of vertexdisjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n
Results 1  10
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4,867