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Deterministic Single Exponential Time Algorithms for Connectivity Problems Parameterized by Treewidth [chapter]

Hans L. Bodlaender, Marek Cygan, Stefan Kratsch, Jesper Nederlof
2013 Lecture Notes in Computer Science  
(FOCS 2011) presented Monte Carlo algorithms for a wide range of connectivity problems running in time c tw |V | O(1) for a small constant c, e.g., for Hamiltonian Cycle and Steiner Tree.  ...  However, for nonlocal problems, like the fundamental class of connectivity problems, for a long time we did not know how to do this faster than tw O(tw) |V | O(1) . Recently, Cygan et al.  ...  Acknowledgements We would like to thank Piotr Sankowski for pointing us to relevant literature of matrixmultiplication time algorithms.  ... 
doi:10.1007/978-3-642-39206-1_17 fatcat:y2kh3fomcrfsnd2hiyqtnoaqia

Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth

Hans L. Bodlaender, Marek Cygan, Stefan Kratsch, Jesper Nederlof
2015 Information and Computation  
(FOCS 2011) presented Monte Carlo algorithms for a wide range of connectivity problems running in time c tw |V | O(1) for a small constant c, e.g., for Hamiltonian Cycle and Steiner Tree.  ...  However, for nonlocal problems, like the fundamental class of connectivity problems, for a long time we did not know how to do this faster than tw O(tw) |V | O(1) . Recently, Cygan et al.  ...  Acknowledgements We would like to thank Piotr Sankowski for pointing us to relevant literature of matrixmultiplication time algorithms.  ... 
doi:10.1016/j.ic.2014.12.008 fatcat:xryaspzrwnc6rncuxegtt2zfzq

Bidimensional Structures: Algorithms, Combinatorics and Logic (Dagstuhl Seminar 13121)

Erik D. Demaine, Fedor V. Fomin, MohammadTaghi Hajiaghayi, Dimitrios M. Thilikos, Marc Herbstritt
2013 Dagstuhl Reports  
The report contains the motivation of the seminar, the abstracts of the talks given during the seminar, and the list of open problems. Seminar 18.-22. March, 2013 -www.dagstuhl.de/13121  ...  We provide a report on the Dagstuhl Seminar 13121: Bidimensional Structures: Algorithms, Combinatorics and Logic held at Schloss Dagstuhl in Wadern, Germany between Monday 18 and Friday 22 of March 2013  ...  More generally, how can we design bounded-treewidth dynamic-programming algorithms for planar completion problems?  ... 
doi:10.4230/dagrep.3.3.51 dblp:journals/dagstuhl-reports/DemaineFHT13 fatcat:vbtdm45hovds5eyorghjbz4kr4

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

Eun Jung Kim, Alexander Langer, Christophe Paul, Felix Reidl, Peter Rossmanith, Ignasi Sau, Somnath Sikdar
2015 ACM Transactions on Algorithms  
Single-exponential algorithms.  ...  Namely, our algorithm runs in time 2 O(k) · n 2 , which is asymptotically optimal with respect to k. So far, single-exponential algorithms were only known for special cases of the family F.  ...  Our gratitude also goes to the anonymous reviewers for thorough comments that improved the presentation of the article.  ... 
doi:10.1145/2797140 fatcat:njyhhxg2q5fyvowl3uryuyr3jy

Linear Kernels and Single-Exponential Algorithms via Protrusion Decompositions [chapter]

Eun Jung Kim, Alexander Langer, Christophe Paul, Felix Reidl, Peter Rossmanith, Ignasi Sau, Somnath Sikdar
2013 Lecture Notes in Computer Science  
Single-exponential algorithms.  ...  Namely, our algorithm runs in time 2 O(k) · n 2 , which is asymptotically optimal with respect to k. So far, single-exponential algorithms were only known for special cases of the family F.  ...  Our gratitude also goes to the anonymous reviewers for thorough comments that improved the presentation of the article.  ... 
doi:10.1007/978-3-642-39206-1_52 fatcat:2gdnwhym6rawniwqgj2lh6xyta

Optimality and tight results in parameterized complexity (Dagstuhl Seminar 14451)

Stefan Kratsch, Daniel Lokshtanov, Dániel Marx, Peter Rossmanith, Marc Herbstritt
2015 Dagstuhl Reports  
Over the last two decades parameterized complexity has become one of the main tools for handling intractable problems.  ...  Recently, tools have been developed not only to classify problems, but also to make statements about how close an algorithm is to being optimal with respect to running time.  ...  We study Graph Motif parameterized by = |V | − k. For general graphs we show that, assuming the strong exponential time hypothesis, a previous O(2 • |E|) time algorithm is optimal.  ... 
doi:10.4230/dagrep.4.11.1 dblp:journals/dagstuhl-reports/KratschLMR14 fatcat:vwgmhttkgrf4pb34jpsb2rfvnm

Parameterized Complexity of Secluded Connectivity Problems [article]

Fedor V. Fomin, Petr A. Golovach, Nikolay Karpov, Alexander S. Kulikov
2015 arXiv   pre-print
Finally, we refine the algorithmic result of Chechik et al. by improving the exponential dependence from the treewidth of the input graph.  ...  We initiate the study of "above guarantee" parameterizations for secluded problems, where the lower bound is given by the size of a Steiner tree.  ...  [8] by showing that Secluded Steiner Treewithout costs can be solved by a randomized algorithm in time that single-exponentially depends on treewidth by applying the Count & Color technique of Cygan  ... 
arXiv:1502.03989v2 fatcat:lruryp2embgixkhyindkjumujq

On Space Efficiency of Algorithms Working on Structural Decompositions of Graphs

Michał Pilipczuk, Marcin Wrochna
2018 ACM Transactions on Computation Theory  
Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms.  ...  Sci., '03], we prove that the question is closely related to a conjecture that the Longest Common Subsequence problem parameterized by the number of input strings does not admit an algorithm that simultaneously  ...  [21] we define 4 N[f poly, f log ] as the class of parameterized problems that can be solved in non-deterministic time f (k)poly(n) and space f (k) log(n) for some computable function f , where k is  ... 
doi:10.1145/3154856 fatcat:6gslgkwqlvbgldsmnzsqn2zgxe

Linear kernels and single-exponential algorithms via protrusion decompositions [article]

Eun Jung Kim, Alexander Langer, Christophe Paul, Felix Reidl, Peter Rossmanith, Ignasi Sau, Somnath Sikdar
2012 arXiv   pre-print
Very recently, an algorithm for Planar-F-Deletion with running time 2^O(k) n ^2 n (such an algorithm is called single-exponential) has been presented in [Fomin et al., FOCS 2012] under the condition that  ...  A parameterized graph problem is called treewidth-bounding if all positive instances have a t-treewidth-modulator of size O(k), for some constant t.  ...  Thilikos, Bruno Courcelle, Daniel Lokshtanov, and Saket Saurabh for interesting discussions and helpful remarks on the manuscript.  ... 
arXiv:1207.0835v2 fatcat:vvquw7fhvvfhdekboqhbkcteau

Parameterized Complexity of Secluded Connectivity Problems

Fedor V. Fomin, Petr A. Golovach, Nikolay Karpov, Alexander S. Kulikov
2016 Theory of Computing Systems  
Finally, we refine the algorithmic result of Chechik et al. by improving the exponential dependence from the treewidth of the input graph.  ...  Similarly, Secluded Steiner Tree is solvable in time O(2 k k 2 · (n + m) log W ). The main result of this paper is about "above guarantee" parameterizations for secluded problems.  ...  Again by the same approach as for Steiner Tree, it is possible to solve Secluded Steiner Tree deterministically in time O((2 + 2 ω+1 ) t · (n + log W ) O(1) ) (here ω is the matrix multiplication constant  ... 
doi:10.1007/s00224-016-9717-x fatcat:kccjizpmerefbdr5hywfkogefq

Solvingd-SAT via Backdoors to Small Treewidth [chapter]

Fedor V. Fomin, Daniel Lokshtanov, Neeldhara Misra, M. S. Ramanujan, Saket Saurabh
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
The new deterministic linear time protrusion replacer has several applications in kernelization and parameterized algorithms.  ...  At first glance, the problem of detecting a weak W ηbackdoor set resembles the algorithmic graph problem of deleting at most k vertices such that the new graph is of treewidth at most t.  ...  Subsequently, we show that there is also a single-exponential deterministic algorithm. Lemma 3.1. Let (A 1 , A 1 ) be a (wb, K η , ρ)-reducer.  ... 
doi:10.1137/1.9781611973730.43 dblp:conf/soda/FominLMRS15 fatcat:4hppsxbm3feybggwnxhjnxv2fq

Randomization in Parameterized Complexity (Dagstuhl Seminar 17041)

Marek Cygan, Fedor V. Fomin, Danny Hermelin, Magnus Wahlström, Marc Herbstritt
2017 Dagstuhl Reports  
Dagstuhl Seminar 17041 "Randomization in Parameterized Complexity" took place from January 22nd to January 27th 2017 with the objective to bridge the gap between randomization and parameterized complexity  ...  We note that extending our algorithmic findings to binary matroids, a superclass of regular matroids, is highly unlikely: Minimum Spanning Circuit parameterized by is W [1] -hard on binary matroids even  ...  More precisely, we prove that Minimum Spanning Circuit parameterized by |T | is W [1] -hard even on cographic matroids, a proper subclass of regular matroids.  ... 
doi:10.4230/dagrep.7.1.103 dblp:journals/dagstuhl-reports/CyganFHW17 fatcat:vjbkuavqdzew3nbk6wjvmpbd5m

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

Michael R. Fellows, Bart M.P. Jansen, Frances Rosamond
2013 European journal of combinatorics (Print)  
We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or  ...  An extensive overview of recent advances on this front is presented for the Vertex Cover problem.  ...  This problem is known to be complete for EXP (deterministic exponential time), so the situation appears discouraging from the standpoint of classical complexity theory [74] .  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

The PACE 2018 Parameterized Algorithms and Computational Experiments Challenge: The Third Iteration

Édouard Bonnet, Florian Sikora, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
The Program Committee of the Third Parameterized Algorithms and Computational Experiments challenge (PACE 2018) reports on the third iteration of the PACE challenge.  ...  In Track B, a tree-decomposition of the graph was provided in the input, and the treewidth was limited. Finally, Track C welcomed heuristics.  ...  We are particularly happy that this edition attracted many people outside the parameterized complexity community, and wish that this will continue for the future editions.  ... 
doi:10.4230/lipics.ipec.2018.26 dblp:conf/iwpec/BonnetS18 fatcat:k5mnkqudevcv5grjckenwoxjji

Solving Connectivity Problems Parameterized by Treedepth in Single-Exponential Time and Polynomial Space

Falko Hegerfeld, Stefan Kratsch, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
(FOCS 2011) showed that connectivity problems parameterized by treewidth can be solved much faster than the previously best known time 𝒪^*(2^{𝒪(twlog tw)}).  ...  Using their inspired Cut&Count technique, they obtained 𝒪^*(α^tw) time algorithms for many such problems.  ...  [11] has provided single-exponential-time and -space algorithms for many connectivity problems parameterized by treewidth.  ... 
doi:10.4230/lipics.stacs.2020.29 dblp:conf/stacs/HegerfeldK20 fatcat:xnyv5llj3nbexd2vvvdpqezhia
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