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802
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
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 sparsification for computing treewidth
 In Proceedings of IPEC
, 2013
"... Abstract. We investigate whether an nvertex instance (G, k) of Treewidth, asking whether the graph G has treewidth at most k, can efficiently be made sparse without changing its answer. By giving a special form of orcrosscomposition, we prove that this is unlikely: if there is an > 0 and a p ..."
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Cited by 3 (0 self)
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. (STACS 2011) to a kernel with O(k2) vertices. Our improved kernel is based on a novel form of treewidthinvariant set. We use the qexpansion lemma of Fomin et al. (STACS 2011) to find such sets efficiently in graphs whose vertex count is superquadratic in their vertex cover number. 1
Degree3 Treewidth Sparsifiers∗
, 2014
"... We study treewidth sparsifiers. Informally, given a graph G of treewidth k, a treewidth sparsifier H is a minor of G, whose treewidth is close to k, V (H)  is small, and the maximum vertex degree in H is bounded. Treewidth sparsifiers of degree 3 are of particular interest, as routing on nodedisj ..."
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Cited by 1 (1 self)
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degree in H is 3. The running time of the algorithm is polynomial in V (G)  and k. Our result is in contrast to the known fact that unless NP ⊆ coNP/poly, treewidth does not admit polynomialsize kernels. One of our key technical tools, which is of independent interest, is a construction of a small
Degree3 Treewidth Sparsifiers
, 2014
"... We study treewidth sparsifiers. Informally, given a graph G of treewidth k, a treewidth sparsifier H is a minor of G, whose treewidth is close to k, V (H)  is small, and the maximum vertex degree in H is bounded. Treewidth sparsifiers of degree 3 are of particular interest, as routing on nodedisj ..."
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degree in H is 3. The running time of the algorithm is polynomial in V (G)  and k. Our result is in contrast to the known fact that unless NP ⊆ coNP/poly, treewidth does not admit polynomialsize kernels. One of our key technical tools, which is of independent interest, is a construction of a small
Monadic datalog over finite structures with bounded treewidth
 IN PROCEEDINGS OF THE TWENTYSIXTH ACM SIGACTSIGMODSIGART SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS (PODS 2007
, 2007
"... Bounded treewidth and Monadic Second Order (MSO) logic have proved to be key concepts in establishing fixedparameter tractability results. Indeed, by Courcelle’s Theorem we know: Any property of finite structures, which is expressible by an MSO sentence, can be decided in linear time (data complexi ..."
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Cited by 9 (4 self)
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complexity) if the structures have bounded treewidth. In principle, Courcelle’s Theorem can be applied directly to construct concrete algorithms by transforming the MSO evaluation problem into a tree language recognition problem. The latter can then be solved via a finite tree automaton (FTA). However
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
 Proceedings 22nd International Colloquium on Automata, Languages and Programming
, 1995
"... We describe the first parallel algorithm with optimal speedup for constructing minimumwidth tree decompositions of graphs of bounded treewidth. On nvertex input graphs, the algorithm works in O((logn)^2) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with opti ..."
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Cited by 33 (9 self)
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with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth, including all decision problems expressible in monadic secondorder logic. On nvertex input graphs, the algorithms use O
Approximate MRF Inference Using Bounded Treewidth Subgraphs
"... Graph cut algorithms [9], commonly used in computer vision, solve a firstorder MRF over binary variables. The state of the art for this NPhard problem is QPBO [1, 2], which finds the values for a subset of the variables in the global minimum. While QPBO is very effective overall there are still ..."
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Cited by 3 (0 self)
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many difficult problems where it can only label a small subset of the variables. We propose a new approach that, instead of optimizing the original graphical model, instead optimizes a tractable submodel, defined as an energy function that uses a subset of the pairwise interactions of the original
Results 1  10
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802