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On finding minimal w-cutset
[article]

2012
*
arXiv
*
pre-print

A w-

arXiv:1207.4127v1
fatcat:ni2xvfne6bce5j7v7j77eixgpe
*cutset*is a generalization of a*cycle*-*cutset*defined as a subset of nodes such that the subgraph*with**cutset*nodes removed has induced-width of w or less. ... It is well-known that the*conditioning*(assigning values)*on*a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. ... Empirically, we show that the minimal*cycle*-*cutset*heuristics based*on*the degree of a node is not competitive*with*the tree-decomposition of the*graph*. ...##
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On computing the minimum feedback vertex set of a directed graph by contraction operations

2000
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

Furthermore, for all ISCAS'89 benchmarks our exact algorithm can find the exact

doi:10.1109/43.833199
fatcat:a3fowx3ffferrmcel3bzrr32jy
*cutsets*in less than 3 s (CPU time)*on*SUN-UltraII workstation. ... This paper is largely concerned*with*three new and powerful reduction operations. ... Please*note*that the approximation*factors*are smaller in the*graphs**with*very low density and the*graphs**with*higher density. ...##
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Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem

1996
*
Artificial Intelligence
*

We test MGA

doi:10.1016/0004-3702(95)00004-6
fatcat:3yh2jmjs7jdpxgxeoctmv3upkm
*on*randomly generated*graphs*and find that the average ratio between the number of instances associated*with*the algorithm's output and the number of instances associated*with*an optimum solution ... We show how to find a small loop*cutset*in a Bayesian network. Finding such a loop*cutset*is the first :itep in the method of*conditioning*for inference. ... We define a*graph*H that consists of the union of these*cycles*-*one**cycle*per each vertex.*Note*that every vertex in F is a linkpoint in H, i.e., a vertex*with*degree 2. ...##
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Toughness, hamiltonicity and split graphs

1996
*
Discrete Mathematics
*

We show that every 3-tough split

doi:10.1016/0012-365x(95)00190-8
fatcat:3vqxxzp2sfc5tlxhqv6xefmt3m
*graph*is hamiltonian and that there is a sequence of nonhamiltonian split*graphs**with*toughness converging to 3. ... Furthermore, we present a polynomial time algorithm deciding whether the toughness of a given split*graph*is less than*one*and show that deciding whether the toughness of a bipartite*graph*is exactly*one*... Katerinis has given a sufficient*condition*for the existence of a 2-*factor*in bipartite*graphs*[21, Theorem 2] implying that every split*graph*G*with*t(G)>~ 3 is 2-*factorable*. ...##
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The traveling salesman problem in graphs with 3-edge cutsets

1985
*
Journal of the ACM
*

*Note*that the triangle (s, v,w) cannot be a

*cycle*of z becaue the removal of these 3 vertices would leave a bipartite

*graph*

*with*

*one*more vertex

*on*

*one*side of the bipartition. ... Therefore finding a A 2-

*factor*of a

*graph*is a set of vertex-disjoint

*cycles*which span the vertices (i.e. every vertex of the

*graph*belongs to exactly

*one*

*cycle*of the 2-

*factor*). ...

##
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Establishing Physical Survivability of Large Networks using Properties of Two-Connected Graphs

2005
*
TENCON 2005 - 2005 IEEE Region 10 Conference
*

This paper presents an alternative technique, based

doi:10.1109/tencon.2005.301226
fatcat:r6lz5fzsojcx5ixy2mqkt4ydqy
*on**graph*theory, for evaluating the physical survivability of networks. ... Some techniques for assessing physical survivability such as the*cutset*method can not deal*with*large size networks [1], [2]. ... If a*graph*is 2-connected, then each vertex of the*graph*will be at least*on**one*of the*cycles*resulting from Alg. 1. Hence, such set of*cycles*is sufficient to verify the survivability of the*graph*. ...##
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Anytime Exact Belief Propagation
[article]

2017
*
arXiv
*
pre-print

In this paper we present work in progress

arXiv:1707.08704v1
fatcat:bsj66st2ojczzmftpxjbuzccki
*on*an Anytime Exact Belief Propagation algorithm that is very similar to Belief Propagation but is exact even for graphical models*with**cycles*, while exhibiting ... In fact, we can take this further and require that these characteristics be present even for probabilistic models*with*probabilities near 0 and 1,*with*graceful degradation as the model becomes more uncertain ...*Note*that each message depends*on*a number of submessages. Since the*factor**graph*is a tree (it has no*cycles*), each sub-message involves a disjoint set of*factors*M j . ...##
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Approximation Algorithms for the Loop Cutset Problem
[article]

2013
*
arXiv
*
pre-print

We test MGA

arXiv:1302.6787v1
fatcat:jeb6elksozg4boinlntigsqj5u
*on*randomly generated*graphs*and find that the average ratio between the number of instances associated*with*the algorithms' output and the number of instances associated*with*a minimum solution ... Finding such a loop*cutset*is the first step in the method of*conditioning*for inference. ... We define a*graph*H that consists of the union of these*cycles*-*one**cycle*per each vertex.*Note*that every vertex in F is a linkpoint in H, i.e., a vertex*with*degree 2. Let B be the vertices of H. ...##
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An Empirical Study of w-Cutset Sampling for Bayesian Networks
[article]

2012
*
arXiv
*
pre-print

In this paper, we investigate performance of w-

arXiv:1212.2449v1
fatcat:ex52uu42gvh5hd7d3u5r37caxa
*cutset*sampling over a range of w values and measure the accuracy of w-*cutset*sampling as a function of w. ... Our experiments demonstrate that the*cutset*sampling idea is quite powerful showing that an optimal balance between inference and sampling benefits substantially from restricting the*cutset*size, even ... A*cycle*-*cutset*of an undirected*graph*is a subset of nodes in the*graph*that, when removed, results in a*graph*without*cycles*. ...##
###
Approximation Algorithms for the Loop Cutset Problem
[chapter]

1994
*
Uncertainty Proceedings 1994
*

We test MGA

doi:10.1016/b978-1-55860-332-5.50013-4
fatcat:o7ziypl57jei7dtgjhqqr4qqbi
*on*randomly generated*graphs*and find that the average ratio between the number of instances associated*with*the algorithms' output and the number of instances associated*with*a minimum solution ... Our algorithm for finding a loop*cutset*, called MGA, finds a loop*cutset*which is guaranteed in the worst case to contain less than twice the number of variables contained in a minimum loop*cutset*. ... The Loop*Cutset*Problem Pearl's method of*conditioning*is*one*of the known inference methods for Bayesian networks. ...##
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Tough graphs and hamiltonian circuits

1973
*
Discrete Mathematics
*

Since a square of a k-connectc;d

doi:10.1016/0012-365x(73)90138-6
fatcat:vexd4udggbgrpfs4q5vfvf5uvm
*graph*is always ktough., a proof of this conjecture*with*to = 2 would imply Fleischner's thec,rem (the square of a block is hamiltonian). ... Clearly, every hamiltonian*graph*is l-tough. Conversely, we conjecture that for some to, ewry to-tough*graph*is hamiltonian. ... Even though its converse does not hold,*one*may wonder what additional*conditions*placed upon a l-tough*graph*G would imply the existence of a hamiltonian*cycle*in G. ...##
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A constraint programming approach to cutset problems

2006
*
Computers & Operations Research
*

We consider the problem of finding a

doi:10.1016/j.cor.2005.01.014
fatcat:6kbeulztcncpjaaryjrpetrelq
*cutset*in a directed*graph*G = (V, E), i.e. a set of vertices that cuts all*cycles*in G. Finding a*cutset*of minimum cardinality is NP-hard. ... We discuss search heuristics based*on**graph*properties provided by the*cutset*constraint, and show the efficiency of the*cutset*constraint*on*benchmarks of the literature for pure minimum*cutset*problems ... vertex set problems, and Mauricio Resende for providing us*with*their GRASP implementation and Funke and Reinelt's benchmarks. ...##
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Tough graphs and hamiltonian circuits

2006
*
Discrete Mathematics
*

Since a square of a k-connected

doi:10.1016/j.disc.2006.03.011
fatcat:ohvy35ngifhqtp4aljnkgrxt74
*graph*is always k-tough, a proof of this conjecture*with*t 0 = 2 would imply Fleischner's theorem (the square of a block is hamiltonian). ... Obviously, a t-tough*graph*is s-tough for all s < t. If G is not complete, then there is a largest t such that G is t-tough; this t will be called the toughness of G and denoted by t (G).*On*the other ... Even though its converse does not hold,*one*may wonder what additional*conditions*placed upon a 1-tough*graph*G would imply the existence of a hamiltonian*cycle*in G. ...##
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Randomized Algorithms for the Loop Cutset Problem

2000
*
The Journal of Artificial Intelligence Research
*

We show how to find a minimum weight loop

doi:10.1613/jair.638
fatcat:xce4drbig5cblhcrufnv36mpsi
*cutset*in a Bayesian network*with*high probability. Finding such a loop*cutset*is the first step in the method of*conditioning*for inference. ... We also show empirically that a variant of this algorithm often finds a loop*cutset*that is closer to the minimum weight loop*cutset*than the*ones*found by the best deterministic algorithms known. ... Part of this work was done while the third author was*on*sabbatical at Microsoft Research. ...##
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On Heuristics for Finding Loop Cutsets in Multiply-Connected Belief Networks
[article]

2013
*
arXiv
*
pre-print

We provide lower bounds

arXiv:1304.1113v1
fatcat:dhp6qcdzubcbdderzcfb3sxz3e
*on*the performance of these algorithms*with*respect to*one*another and*with*respect to optimal. ... We introduce a new heuristic algorithm for the problem of finding minimum size loop*cutsets*in multiply connected belief networks. ...*Note*that since instanti ating the loop*cutset*reduces the belief network to a singly connected network, Pearl's efficient algorithms for such networks can be applied to compute each of the above*factors*...
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