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For the vast majority of local graph problems standard dynamic programming techniques give c^tw V^O(1) algorithms, where tw is the treewidth of the input graph.
The design and analysis of factorial experiments
F. Yates · 1937
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The factorization of linear graphs
W. T. Tutte · 1947
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The Traveling Salesman Problem and Minimum Spanning Trees
Micheal Held and Richard M. Karp · 1970
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The Traveling-Salesman Problem and Minimum Spanning Trees: Part II
Micheal Held and Richard M. Karp · 1971
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Reducibility Among Combinatorial Problems
Richard M. Karp · 1972
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A Probabilistic Remark on Algebraic Program Testing
Richard A. DeMillo and Richard J. Lipton · 1978
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Probabilistic algorithms for sparse polynomials
Richard Zippel · 1979
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Fast Probabilistic Algorithms for Verification of Polynomial Identities
Jack. T. Schwartz · 1980
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Graph minors. III. Planar tree-width
Neil Robertson and Paul D. Seymour · 1984
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Matching is as easy as matrix inversion
Ketan Mulmuley, Umesh V. Vazirani, and Vijay V. Vazirani · 1987
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NP-completeness and degree restricted spanning trees
Robert James Douglas · 1992
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Fixed Parameter Tractability and Completeness
Rodney G. Downey and Michael R. Fellows · 1992
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On Disjoint Cycles
Hans L. Bodlaender · 1994
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Treewidth, Computations and Approximations
Ton Kloks · 1994
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Randomness-Optimal Unique Element Isolation with Applications to Perfect Matching and Related Problems
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Mixed Searching and Proper-Path-Width
Atsushi Takahashi, Shuichi Ueno, and Yoji Kajitani · 1995
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In Parameterized Complexity
Rodney G. Downey and Michael R. Fellows · 1999
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Randomized Algorithms for the Loop Cutset Problem
Ann Becker, Reuven Bar-Yehuda, and Dan Geiger · 2000
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Diameter and treewidth in minor-closed graph families
David Eppstein · 2000
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Introduction to automata theory, languages, and computation - (2. ed.)
John E. Hopcroft, Rajeev Motwani, and Jeffrey D. Ullman · 2001
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On the Complexity of k-SAT
Russell Impagliazzo and Ramamohan Paturi · 2001
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Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set
Venkatesh Raman, Saket Saurabh, and C. R. Subramanian · 2002
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Primality and identity testing via Chinese remaindering
Manindra Agrawal and Somenath Biswas · 2003
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A Simple and Fast Approach for Solving Problems on Planar Graphs
Fedor V. Fomin. and Dimitrios M. Thilikos · 2004
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Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds
Valentine Kabanets and Russell Impagliazzo · 2004
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Parameterized Algorithms for Feedback Vertex Set
Iyad A. Kanj, Michael J. Pelsmajer, and Marcus Schaefer · 2004
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Finding odd cycle transversals
Bruce A. Reed, Kaleigh Smith, and Adrian Vetta · 2004
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Graph Minors XX. Wagner’s conjecture
Neil Robertson and Paul D. Seymour · 2004
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Combinatorial Optimization on Graphs of Bounded Treewidth
Hans L. Bodlaender and Arie M. C. A. Koster · 2008
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Improved algorithms for feedback vertex set problems
Jianer Chen, Fedor V. Fomin, Yang Liu, Songjian Lu, and Yngve Villanger · 2008
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Catalan structures and dynamic programming in H-minor-free graphs
Frederic Dorn, Fedor V. Fomin, and Dimitrios M. Thilikos · 2008
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H. Gebauer · 2008
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Faster Algebraic Algorithms for Path and Packing Problems
Ioannis Koutis · 2008
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Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover
Daniel Mölle, Stefan Richter, and Peter Rossmanith · 2008
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An O(2 o(k) {}^{\mbox{{o}(k)}} n 3 {}^{\mbox{3}} ) FPT Algorithm for the Undirected Feedback Vertex Set Problem
Frank K. H. A. Dehne, Michael R. Fellows, Michael A. Langston, Frances A. Rosamond, and Kim Stevens · 2005
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The bidimensionality Theory and Its Algorithmic Applications
Erik D. Demaine and Mohammadtaghi Hajiaghayi · 2005
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Efficient exact algorithms on planar graphs: Exploiting sphere cut branch decompositions
Frederic Dorn, Eelko Penninkx, Hans L. Bodlaender, and Fedor V. Fomin · 2005
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Branch and tree decomposition techniques for discrete optimization
Illya V. Hicks, Arie M. C. A. Koster, and Elif Kolotoǧlu · 2005
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Jon Kleinberg and Eva Tardos · 2005
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Cutwidth I: A linear time fixed parameter algorithm
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Fast fast
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Limits and Applications of Group Algebras for Parameterized Problems
Ioannis Koutis and Ryan Williams · 2009
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Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution
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Inclusion/Exclusion Meets Measure and Conquer
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Finding paths of length k in O * {}^{\mbox{*}} (2 k {}^{\mbox{k}} ) time
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Amortized Analysis of Exponential Time and Parameterized Algorithms: Measure and Conquer and Reference Search Trees
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Determinant Sums for Undirected Hamiltonicity
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Narrow sieves for parameterized paths and packings
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A Bottom-Up Method and Fast Algorithms for max independent set
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An improved LP-based approximation for steiner tree
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On Feedback Vertex Set New Measure and New Structures
Yixin Cao, Jianer Chen, and Yang Liu · 2010
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Exact and approximate bandwidth
Marek Cygan and Marcin Pilipczuk · 2010
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Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs
Frederic Dorn, Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, and Saket Saurabh · 2010
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FPT Algorithms for Connected Feedback Vertex Set
Neeldhara Misra, Geevarghese Philip, Venkatesh Raman, Saket Saurabh, and Somnath Sikdar · 2010
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Known Algorithms on Graphs of Bounded Treewidth are Probably Optimal
Daniel Lokshtanov, Daniel Marx, and Saket Saurabh · 2011
Closest in time.
Slightly Superexponential Parameterized Problems
Daniel Lokshtanov, Daniel Marx, and Saket Saurabh · 2011
Closest in time.