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On finding minimal w-cutset [article]

Bozhena Bidyuk, Rina Dechter
2012 arXiv   pre-print
A w-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.  ... 
arXiv:1207.4127v1 fatcat:ni2xvfne6bce5j7v7j77eixgpe

On computing the minimum feedback vertex set of a directed graph by contraction operations

Hen-Ming Lin, Jing-Yang Jou
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 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.  ... 
doi:10.1109/43.833199 fatcat:a3fowx3ffferrmcel3bzrr32jy

Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem

Ann Becker, Dan Geiger
1996 Artificial Intelligence  
We test MGA 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.  ... 
doi:10.1016/0004-3702(95)00004-6 fatcat:3yh2jmjs7jdpxgxeoctmv3upkm

Toughness, hamiltonicity and split graphs

Dieter Kratsch, Jenő Lehel, Haiko Müller
1996 Discrete Mathematics  
We show that every 3-tough split 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.  ... 
doi:10.1016/0012-365x(95)00190-8 fatcat:3vqxxzp2sfc5tlxhqv6xefmt3m

The traveling salesman problem in graphs with 3-edge cutsets

G. Cornuéjols, D. Naddef, W. Pulleyblank
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).  ... 
doi:10.1145/3149.3154 fatcat:lox64fjxwzb2rnja2ftqaycgwi

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

Daryoush Habibi, Hoang Nguyen, Quoc Phung, Kung-meng Lo
2005 TENCON 2005 - 2005 IEEE Region 10 Conference  
This paper presents an alternative technique, based 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.  ... 
doi:10.1109/tencon.2005.301226 fatcat:r6lz5fzsojcx5ixy2mqkt4ydqy

Anytime Exact Belief Propagation [article]

Gabriel Azevedo Ferreira, Quentin Bertrand, Charles Maussion, Rodrigo de Salvo Braz
2017 arXiv   pre-print
In this paper we present work in progress 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 .  ... 
arXiv:1707.08704v1 fatcat:bsj66st2ojczzmftpxjbuzccki

Approximation Algorithms for the Loop Cutset Problem [article]

Ann Becker, Dan Geiger
2013 arXiv   pre-print
We test MGA 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.  ... 
arXiv:1302.6787v1 fatcat:jeb6elksozg4boinlntigsqj5u

An Empirical Study of w-Cutset Sampling for Bayesian Networks [article]

Bozhena Bidyuk, Rina Dechter
2012 arXiv   pre-print
In this paper, we investigate performance of w-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.  ... 
arXiv:1212.2449v1 fatcat:ex52uu42gvh5hd7d3u5r37caxa

Approximation Algorithms for the Loop Cutset Problem [chapter]

Ann Becker, Dan Geiger
1994 Uncertainty Proceedings 1994  
We test MGA 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.  ... 
doi:10.1016/b978-1-55860-332-5.50013-4 fatcat:o7ziypl57jei7dtgjhqqr4qqbi

Tough graphs and hamiltonian circuits

V. Chvátal
1973 Discrete Mathematics  
Since a square of a k-connectc;d 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.  ... 
doi:10.1016/0012-365x(73)90138-6 fatcat:vexd4udggbgrpfs4q5vfvf5uvm

A constraint programming approach to cutset problems

François Fages, Akash Lal
2006 Computers & Operations Research  
We consider the problem of finding a 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.  ... 
doi:10.1016/j.cor.2005.01.014 fatcat:6kbeulztcncpjaaryjrpetrelq

Tough graphs and hamiltonian circuits

V. Chvátal
2006 Discrete Mathematics  
Since a square of a k-connected 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.  ... 
doi:10.1016/j.disc.2006.03.011 fatcat:ohvy35ngifhqtp4aljnkgrxt74

Randomized Algorithms for the Loop Cutset Problem

A. Becker, R. Bar-Yehuda, D. Geiger
2000 The Journal of Artificial Intelligence Research  
We show how to find a minimum weight loop 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.  ... 
doi:10.1613/jair.638 fatcat:xce4drbig5cblhcrufnv36mpsi

On Heuristics for Finding Loop Cutsets in Multiply-Connected Belief Networks [article]

Jonathan Stillman
2013 arXiv   pre-print
We provide lower bounds 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  ... 
arXiv:1304.1113v1 fatcat:dhp6qcdzubcbdderzcfb3sxz3e
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