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18,659
Codes and Decoding on General Graphs
, 1996
"... Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithm ..."
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Cited by 359 (1 self)
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algorithms are special cases of two generic algorithms, the minsum and sumproduct algorithms, which also include noniterative algorithms such as Viterbi decoding. The minsum and sumproduct algorithms are developed and presented as generalized trellis algorithms, where the time axis of the trellis
An algorithm for drawing general undirected graphs
 Information Processing Letters
, 1989
"... Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets, and entit ..."
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Cited by 698 (2 self)
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Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets
Partitioning Properties of General Graphs
, 2003
"... this technical report, we will make an abstraction of the circuit concept, and focus on the partitioning properties of general graphs ..."
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Cited by 1 (0 self)
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this technical report, we will make an abstraction of the circuit concept, and focus on the partitioning properties of general graphs
On extremal problems of graphs and generalized graphs
 Israel J. Math
, 1964
"... An rgraph is a graph whose basic elements are its vertices and rtuples. It is proved that to every 1 and r there is an e(l, r) so that for n> no every rgraph of n vertices and n 'E(i, r) rtuples contains r. /vertices P),I5 j < r, l < i < l, so that all the rtuples (x i, ( 1), ..."
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Cited by 99 (1 self)
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An rgraph is a graph whose basic elements are its vertices and rtuples. It is proved that to every 1 and r there is an e(l, r) so that for n> no every rgraph of n vertices and n 'E(i, r) rtuples contains r. /vertices P),I5 j < r, l < i < l, so that all the rtuples (x i, ( 1
What energy functions can be minimized via graph cuts?
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2004
"... In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are co ..."
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Cited by 1047 (23 self)
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are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes
GENERATORS OF GENERALIZED GRAPH IDEALS
"... Abstract. This work deals with the way to determine, in the degree q66, how many paths of length (q−1) are contained in a connected graph G, using only its incidence matrix. The composition of such paths and the generators of the generalized graph ideals relative to G are studied for every degree q. ..."
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Abstract. This work deals with the way to determine, in the degree q66, how many paths of length (q−1) are contained in a connected graph G, using only its incidence matrix. The composition of such paths and the generators of the generalized graph ideals relative to G are studied for every degree q
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems
Fully generalized graph cores
"... Abstract. A core in a graph is usually taken as a set of highly connected vertices. Although general, this definition is intuitive and useful for studying the structure of many real networks. Nevertheless, depending on the problem, different formulations of graph core may be required, leading us t ..."
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Abstract. A core in a graph is usually taken as a set of highly connected vertices. Although general, this definition is intuitive and useful for studying the structure of many real networks. Nevertheless, depending on the problem, different formulations of graph core may be required, leading us
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 534 (11 self)
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to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings
Results 1  10
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18,659