Results 1  10
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5,060
The complexity of theoremproving procedures
 IN STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministi ..."
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Cited by 1050 (5 self)
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of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite
Gradientbased learning applied to document recognition
 Proceedings of the IEEE
, 1998
"... Multilayer neural networks trained with the backpropagation algorithm constitute the best example of a successful gradientbased learning technique. Given an appropriate network architecture, gradientbased learning algorithms can be used to synthesize a complex decision surface that can classify hi ..."
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Cited by 1533 (84 self)
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to deal with the variability of two dimensional (2D) shapes, are shown to outperform all other techniques. Reallife document recognition systems are composed of multiple modules including field extraction, segmentation, recognition, and language modeling. A new learning paradigm, called graph
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul
NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs
Pebbling graphs of fixed diameter
 J. Graph Theory
, 2014
"... Abstract Given a configuration of indistinguishable pebbles on the vertices of a connected graph G on n vertices, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one pebble on an adjacent vertex. The mpebbling number of a graph G, πm(G), is the small ..."
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Cited by 2 (2 self)
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Abstract Given a configuration of indistinguishable pebbles on the vertices of a connected graph G on n vertices, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one pebble on an adjacent vertex. The mpebbling number of a graph G, πm
Complexity of finding embeddings in a ktree
 SIAM JOURNAL OF DISCRETE MATHEMATICS
, 1987
"... A ktree is a graph that can be reduced to the kcomplete graph by a sequence of removals of a degree k vertex with completely connected neighbors. We address the problem of determining whether a graph is a partial graph of a ktree. This problem is motivated by the existence of polynomial time al ..."
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Cited by 386 (1 self)
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algorithms for many combinatorial problems on graphs when the graph is constrained to be a partial ktree for fixed k. These algorithms have practical applications in areas such as reliability, concurrent broadcasting and evaluation of queries in a relational database system. We determine the complexity
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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is replaced by an arbitrary graph, the "Tanner graph". With cyclefree Tanner graphs, the resulting decoding algorithms (e.g., Viterbi decoding) are maximumlikelihood but suffer from an exponentially increasing complexity. Iterative decoding occurs when the Tanner graph has cycles (e.g., turbo
A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 373 (15 self)
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complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching
Graph evolution: Densification and shrinking diameters
 ACM TKDD
, 2007
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 267 (16 self)
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that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks
Pebbling in Diameter Two Graphs and Products of Paths
 J. Graph Th
, 1997
"... Results regarding the pebbling number of various graphs are presented. We say a graph is of Class 0 if its pebbling number equals the number of its vertices. For diameter d we conjecture that every graph of sufficient connectivity is of Class 0. We verify the conjecture for d = 2 by characterizin ..."
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Cited by 32 (15 self)
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Results regarding the pebbling number of various graphs are presented. We say a graph is of Class 0 if its pebbling number equals the number of its vertices. For diameter d we conjecture that every graph of sufficient connectivity is of Class 0. We verify the conjecture for d = 2
Results 1  10
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5,060