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455
An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1993
"... A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices. Cl ..."
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Cited by 360 (0 self)
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A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices
How to prove a theorem so no one else can claim it
 In: Proceedings of the International Congress of Mathematicians
, 1987
"... Goldwasser, Micali, and Rackoff [GMR] define for us what it means for a theorem to have a "zeroknowledge proof. " In brief, a zeroknowledge proof is an interactive probabilistic protocol that gives highly convincing (but not absolutely certain) evidence that a theorem is true and that th ..."
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Cited by 142 (0 self)
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that the theorem is true. GMW start by considering a particular NPcomplete problem: Graph 3Colorability. Instance. A graph G. Question. Can G be "properly " 3colored (each node colored by one of 3 given colors so that no two adjacent nodes receive the same color). GMW show that a "prover "
Efficient Testing of Large Graphs
 Combinatorica
"... Let P be a property of graphs. An test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case that it h ..."
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Cited by 176 (47 self)
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Let P be a property of graphs. An test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case
Three Theorems regarding Testing Graph Properties
, 2001
"... Property testing is a relaxation of decision problems in which it is required to distinguish yesinstances (i.e., objects having a predetermined property) from instances that are far from any yesinstance. We presents three theorems regarding testing graph properties in the adjacency matrix represe ..."
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Cited by 87 (13 self)
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Property testing is a relaxation of decision problems in which it is required to distinguish yesinstances (i.e., objects having a predetermined property) from instances that are far from any yesinstance. We presents three theorems regarding testing graph properties in the adjacency matrix
A proof of Alon’s second eigenvalue conjecture
, 2003
"... A dregular graph has largest or first (adjacency matrix) eigenvalue λ1 = d. Consider for an even d ≥ 4, a random dregular graph model formed from d/2 uniform, independent permutations on {1,...,n}. We shall show that for any ɛ>0 we have all eigenvalues aside from λ1 = d are bounded by 2 √ d − 1 ..."
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Cited by 166 (1 self)
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A dregular graph has largest or first (adjacency matrix) eigenvalue λ1 = d. Consider for an even d ≥ 4, a random dregular graph model formed from d/2 uniform, independent permutations on {1,...,n}. We shall show that for any ɛ>0 we have all eigenvalues aside from λ1 = d are bounded by 2 √ d
An Adjacency Criterion for Coxeter Matroids
"... Introduction. This paper continues a series of investigations [2, 3, 6, 7, 8, 11, 20] devoted to the systematic development of the theory of Coxeter matroids. The main result of the present paper (Theorem 1.2) concerns a geometric characterization of Coxeter matroids. It is used in the subsequent p ..."
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Cited by 6 (5 self)
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Introduction. This paper continues a series of investigations [2, 3, 6, 7, 8, 11, 20] devoted to the systematic development of the theory of Coxeter matroids. The main result of the present paper (Theorem 1.2) concerns a geometric characterization of Coxeter matroids. It is used in the subsequent
WynerZiv Coding of Motion Video
 in Proc. Asilomar Conference on Signals and Systems
, 2002
"... In current interframe video compression systems, the encoder performs predictive coding to exploit the similarities of successive frames. The WynerZiv Theorem on source coding with side information available only at the decoder suggests that an asymmetric video codec, where individual frames are en ..."
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Cited by 147 (17 self)
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In current interframe video compression systems, the encoder performs predictive coding to exploit the similarities of successive frames. The WynerZiv Theorem on source coding with side information available only at the decoder suggests that an asymmetric video codec, where individual frames
Adjacency preserving mappings of rectangular matrices
 Beiträge Algebra Geom
"... Abstract. Let D be a division ring and let m,n be integers ≥ 2. Let Mm×n(D) be the space of m × n matrices. In the fundamental theorem of the geometry of rectangular matrices all bijective mappings ϕ of Mm×n(D) are determined such that both ϕ and ϕ−1 preserve adjacency. We show that if a bijective m ..."
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Cited by 6 (1 self)
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Abstract. Let D be a division ring and let m,n be integers ≥ 2. Let Mm×n(D) be the space of m × n matrices. In the fundamental theorem of the geometry of rectangular matrices all bijective mappings ϕ of Mm×n(D) are determined such that both ϕ and ϕ−1 preserve adjacency. We show that if a bijective
An update on the fourcolor theorem
 Notices of the AMS
, 1998
"... very planar map of connected countries can be colored using four colors in such a way that countries with a common boundary segment (not just a point) receive different colors. It is amazing that such a simply stated result resisted proof for one and a quarter centuries, and even today it is not ye ..."
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Cited by 28 (5 self)
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that four colors sufficed. He asked his brother Frederick if it was true that any map can be colored using four colors in such a way that adjacent regions (i.e., those sharing a common boundary segment, not just a point) receive different colors. Frederick Guthrie then communicated the conjecture to De
Locally restricted compositions I. Restricted adjacent differences
 Elec. J. Combin
"... We study compositions of the integer n in which the first part, successive differences, and the last part are constrained to lie in prescribed sets L, D, R, respectively. A simple condition on D guarantees that the generating function f(x, L, D, R) has only a simple pole on its circle of convergence ..."
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Cited by 13 (3 self)
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of convergence and this at r(D), a function independent of L and R. Thus the number of compositions is asymptotic to Ar(D) −n for a suitable constant A = A(L, D, R). We prove a multivariate central and local limit theorem and apply it to various statistics of random locally restricted compositions of n
Results 1  10
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455