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CARDINALITY OF A MINIMAL FORBIDDEN GRAPH FAMILY FOR REDUCIBLE ADDITIVE HEREDITARY GRAPH PROPERTIES
"... An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let La denote a class of all such properties. In the paper, we consider Hreducible over La properties with H being a xed graph. The niteness of the sets of all minima ..."
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Cited by 1 (1 self)
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An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let La denote a class of all such properties. In the paper, we consider Hreducible over La properties with H being a xed graph. The niteness of the sets of all
An extension of the ShihDong's combinatorial xed point theorem
"... Abstract: Shih and Dong have proved a boolean analogue of the Jacobian problem: if a map from f0; 1gn to itself has the property that all the boolean eigenvalues of the discrete Jacobian matrix of each element of f0; 1gn are zero, then it has a unique xed point. In this note, this result is extended ..."
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Abstract: Shih and Dong have proved a boolean analogue of the Jacobian problem: if a map from f0; 1gn to itself has the property that all the boolean eigenvalues of the discrete Jacobian matrix of each element of f0; 1gn are zero, then it has a unique xed point. In this note, this result
Deciding FirstOrder Properties of Locally TreeDecomposable Graphs
 In Proc. 26th ICALP
, 1999
"... . We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable cl ..."
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Cited by 98 (14 self)
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intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of treewidth of a graph. 3Colorability, Hamiltonicity, and many other NPcomplete properties of graphs can be decided in linear time when restricted to graphs whose treewidth is bounded by a xed
Energy minimization using multiple supply voltages
 In International Symposium on Low Power Electronics and Design
, 1996
"... AbstractWe present a dynamic programming technique for solving the multiple supply voltage scheduling problem in both nonpipelined and functionally pipelined datapaths. The scheduling problem refers to the assignment of a supply voltage level (selected from a xed and known number of voltage level ..."
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Cited by 146 (5 self)
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AbstractWe present a dynamic programming technique for solving the multiple supply voltage scheduling problem in both nonpipelined and functionally pipelined datapaths. The scheduling problem refers to the assignment of a supply voltage level (selected from a xed and known number of voltage
Graph separators: a parameterized view
 Journal of Computer and System Sciences
, 2001
"... Graph separation is a wellknown tool to make (hard) graph problems accessible to a divide and conquer approach. We show how to use graph separator theorems in combination with (linear) problem kernels in order to develop xed parameter algorithms for many wellknown NPhard (planar) graph problems. ..."
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Cited by 29 (12 self)
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Graph separation is a wellknown tool to make (hard) graph problems accessible to a divide and conquer approach. We show how to use graph separator theorems in combination with (linear) problem kernels in order to develop xed parameter algorithms for many wellknown NPhard (planar) graph problems
A DoubleLoop Algorithm to Minimize the Bethe and Kikuchi Free Energies
 NEURAL COMPUTATION
, 2001
"... Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail t ..."
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Cited by 137 (5 self)
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Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail
Evaluating the Tutte Polynomial for Graphs of Bounded TreeWidth
, 1998
"... ... all but eight specic points and one specic curve of the (x; y)plane. In contrast we show that if k is a xed constant then for graphs of treewidth at most k there is an algorithm that will evaluate the polynomial at any point using only a linear number of multiplications and additions. ..."
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Cited by 35 (2 self)
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... all but eight specic points and one specic curve of the (x; y)plane. In contrast we show that if k is a xed constant then for graphs of treewidth at most k there is an algorithm that will evaluate the polynomial at any point using only a linear number of multiplications and additions.
TreeBased Reparameterization for Approximate Estimation on Loopy Graphs
 Advances in Neural Information Processing Systems (NIPS
, 2001
"... We present a treebased reparameterization framework that provides a new conceptual view of a large class of iterative algorithms for computing approximate marginals in graphs with cycles. It includes belief propagation (BP), which can be reformulated as a very local form of reparameterization. Mor ..."
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Cited by 53 (6 self)
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We present a treebased reparameterization framework that provides a new conceptual view of a large class of iterative algorithms for computing approximate marginals in graphs with cycles. It includes belief propagation (BP), which can be reformulated as a very local form of reparameterization
The power of small coalitions in graphs
 In Proc. of 2nd Colloquium on Structural Information and Communication Complexity
, 1995
"... This paper considers the question of the in uence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of ..."
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Cited by 17 (2 self)
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This paper considers the question of the in uence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function
Preliminaries On The Asymptotic Number Of HFree Labeled Connected Graphs with a Given Number of Vertices and Edges
"... . Given a xed set = fH 1 ..."
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