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2,673
Locally constrained homomorphisms on graphs of bounded degree and bounded treewidth
, 2013
"... A homomorphism from a graph G to a graph H is locally bijective, injective, or surjective if its restriction to the neighborhood of every vertex of G is bijective, injective, or surjective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given ..."
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given graph H that is locally bijective, injective or surjective, respectively, are NPcomplete even when G has bounded pathwidth or when both G and H are of bounded maximum degree. We complement these hardness results by showing that the three problems are polynomialtime solvable if G has bounded
A Partial KArboretum of Graphs With Bounded Treewidth
 J. Algorithms
, 1998
"... The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes ..."
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Cited by 328 (34 self)
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The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between
Dynamic Programming On Graphs With Bounded Treewidth
, 1987
"... In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth _< k, (or equivalently, the class of partial ktrees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses CLCC, and CECC. We show that ea ..."
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Cited by 72 (1 self)
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that each problem in LCC (or CLCC) is solvable in polynomial (O(nc)) time, when restricted to graphs with fixed up perbounds on the treewidth and degree; and that each problem in ECC (or CECC) is solvable in polynomial (O(nc)) time, when re stricted to graphs with a fixed upperbound on the treewidth
On Bounded Treewidth Duality of Graphs
, 1999
"... We prove that for any integers m; k, there is an integer n0 such that if G is a graph of girth n0 then any partial ktree homomorphic to G is also homomorphic to C2m+1 . As a corollary, every nonbipartite graph does not have bounded treewidth duality. ..."
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Cited by 9 (2 self)
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We prove that for any integers m; k, there is an integer n0 such that if G is a graph of girth n0 then any partial ktree homomorphic to G is also homomorphic to C2m+1 . As a corollary, every nonbipartite graph does not have bounded treewidth duality.
Algorithms for Graphs of (Locally) Bounded Treewidth
, 2001
"... Many reallife problems can be modeled by graphtheoretic problems. These graph problems are usually NPhard and hence there is no efficient algorithm for solving them, unless P= NP. One way to overcome this hardness is to solve the problems when restricted to special graphs. Trees are one kind of g ..."
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Cited by 4 (3 self)
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of graph for which several NPcomplete problems can be solved in polynomial time. Graphs of bounded treewidth, which generalize trees, show good algorithmic properties similar to those of trees. Using ideas developed for tree algorithms, Arnborg and Proskurowski introduced a general dynamic programming
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Lower Bounds for the Graph Homomorphism Problem?
"... Abstract. The graph homomorphism problem (HOM) asks whether the vertices of a given nvertex graph G can be mapped to the vertices of a given hvertex graph H such that each edge of G is mapped to an edge of H. The problem generalizes the graph coloring problem and at the same time can be viewed as ..."
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Cited by 1 (1 self)
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Ω(vc(G)) shows that the upper bound is asymptotically tight. As to the properties of the “righthand side ” graph H, it is known that HOM(G,H) can be solved in time (f(∆(H)))n and (f(tw(H)))n where ∆(H) is the maximum degree of H and tw(H) is the treewidth ofH. This gives singleexponential algorithms for graphs
Results 1  10
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2,673