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On the Power of Tree-Depth for Fully Polynomial FPT Algorithms [article]

Yoichi Iwata, Tomoaki Ogasawara, Naoto Ohsaka
2017 arXiv   pre-print
(SODA 2017) introduced the concept of fully polynomial FPT algorithms.  ...  Especially, we solve an open problem of fully polynomial FPT algorithm for Weighted Matching parameterized by tree-width posed by Fomin et al.  ...  Acknowledgement We would like to thank Hiroshi Imai for pointing out to us the reference [21] .  ... 
arXiv:1710.04376v2 fatcat:l7bcdthq2zg4phw5mjcxwo2ata

On the Power of Tree-Depth for Fully Polynomial FPT Algorithms

Yoichi Iwata, Tomoaki Ogasawara, Naoto Ohsaka
unpublished
Especially, we solve an open problem of fully polynomial FPT algorithm for Weighted Matching parameterized by tree-width posed by Fomin et al.  ...  tree-depth of the input graph.  ...  Gabow [12] obtained the O(n(m + n log n))-time algorithm by iteratively applying the following lemma. 41:8 On the Power of Tree-Depth for Fully Polynomial FPT Algorithms 3 in O(m + n log n) time.  ... 
fatcat:ipkqeo4yl5hvta2lwryrulnkrq

Digraph width measures in parameterized algorithmics

Robert Ganian, Petr Hliněný, Joachim Kneis, Alexander Langer, Jan Obdržálek, Peter Rossmanith
2014 Discrete Applied Mathematics  
On the positive side, we also note that taking Kanté's directed generalization of rank-width as a parameter makes many problems fixed parameter tractable.  ...  Several recent papers, e.g. those of Kreutzer-Ordyniak, Dankelmann-Gutin-Kim, or Lampis-Kaouri-Mitsou, have given some evidence for this.  ...  This work has been supported by a Czech-German bilateral grant of GAČR and DFG (201/09/J021 and RO 927/9). Moreover, P. Hliněný has been supported by the Czech research grant GAČR 201/08/0308.  ... 
doi:10.1016/j.dam.2013.10.038 fatcat:jw3g26o5gvc7dnk4mhsp2nnmkm

Computing Kernels in Parallel: Lower and Upper Bounds

Max Bannach, Till Tantau, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
An intriguing finding is that there are complex trade-offs between kernel size and the depth of the circuits needed to compute them: For the vertex cover problem, an exponential kernel can be computed  ...  Other natural problems for which similar (but quantitatively different) effects can be observed include tree decomposition problems parameterized by the vertex cover number, the undirected feedback vertex  ...  Computing a Kernel for Tree Depth. The last problem we consider is tree depth, and, as for path width, we prove a version of Theorem 5.3 for it.  ... 
doi:10.4230/lipics.ipec.2018.13 dblp:conf/iwpec/BannachT18 fatcat:lcfh73xwyngjla4x34bjxwdg3a

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.  ...  Well-Quasi-Ordering One of the most powerful FPT classification tools is well-quasi-ordering (wqo).  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

Improving Vertex Cover as a Graph Parameter

Robert Ganian
2015 Discrete Mathematics & Theoretical Computer Science  
In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that  ...  Apart from introducing the parameter itself, this article provides a number of new FPT algorithms parameterized by twin-cover with a special emphasis on solving problems which are not in FPT even when  ...  of vertices on fire in time O(|V |). 2 Other FPT and kernelization algorithms FPT algorithms for problems hard on clique-width Here we present two FPT algorithms for problems which are not in FPT  ... 
doi:10.46298/dmtcs.2136 fatcat:z3viox6nwvaojc3iibyikwqywu

Computing Kernels in Parallel: Lower and Upper Bounds [article]

Max Bannach, Till Tantau
2018 arXiv   pre-print
An intriguing finding is that there are complex trade-offs between kernel size and the depth of the circuits needed to compute them: For the vertex cover problem, an exponential kernel can be computed  ...  Other natural problems for which similar (but quantitatively different) effects can be observed include tree decomposition problems parameterized by the vertex cover number, the undirected feedback vertex  ...  Perhaps even more challenging seems to be the design of a framework for proving that polynomially sized kernels for these problems cannot be computed in AC 0 .  ... 
arXiv:1807.03604v1 fatcat:t4zqkehl2vd6hfxs3flmsj6zlu

Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints

Daniel Karapetyan, Andrew J. Parkes, Gregory Gutin, Andrei Gagarin
2019 The Journal of Artificial Intelligence Research  
Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm and also has only polynomial-space complexity  ...  on the assignment.  ...  The source codes of the instance generator and PBT, as well as the experimental data, are publicly available [36].  ... 
doi:10.1613/jair.1.11339 fatcat:lr4bl4gfczh4biqv32szgxntzm

A Basic Parameterized Complexity Primer [chapter]

Rod Downey
2012 Lecture Notes in Computer Science  
Research supported by the Marsden Fund of New Zealand. Dedicated to my old friend Mike on the occasion of his 60th Birthday.  ...  Whilst not doing the area justice, the basics of the techniques for proving tractability, establishing hardness, and the philosophy are given.  ...  In each case the algorithmic metatheorem gives algorithms where each alternation of quantifier (roughly) gives another power of two in towers of powers of two for the constants.  ... 
doi:10.1007/978-3-642-30891-8_9 fatcat:fpq3zvaccfcavaxomwkeh5tyby

The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number

Michael Fellows, Daniel Lokshtanov, Neeldhara Misra, Matthias Mnich, Frances Rosamond, Saket Saurabh
2009 Theory of Computing Systems  
We do two things: (1) We describe much improved FPT algorithms for a large number of graph problems, for input graphs G for which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically  ...  The max leaf number ml(G) of a connected graph G is the maximum number of leaves in a spanning tree for G.  ...  Systematically Attacking a Row: Well-Quasiordering One of the most powerful FPT classification tools is well-quasiordering.  ... 
doi:10.1007/s00224-009-9167-9 fatcat:ezqsz2ggzzgd5iicukjjenzoai

The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number [chapter]

Michael Fellows, Frances Rosamond
2007 Lecture Notes in Computer Science  
We do two things: (1) We describe much improved FPT algorithms for a large number of graph problems, for input graphs G for which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically  ...  The max leaf number ml(G) of a connected graph G is the maximum number of leaves in a spanning tree for G.  ...  Systematically Attacking a Row: Well-Quasiordering One of the most powerful FPT classification tools is well-quasiordering.  ... 
doi:10.1007/978-3-540-73001-9_28 fatcat:6ctmbq7kgrbfpeer6mpc5pqaja

When Trees Grow Low: Shrubs and Fast MSO1 [chapter]

Robert Ganian, Petr Hliněný, Jaroslav Nešetřil, Jan Obdržálek, Patrice Ossona de Mendez, Reshma Ramadurai
2012 Lecture Notes in Computer Science  
Recent characterization [9] of those graphs for which coloured MSO2 model checking is fast raised the interest in the graph invariant called tree-depth.  ...  To prove that MSO1 model checking is fast for classes of bounded shrub-depth, we show that shrub-depth exactly characterizes the graph classes having interpretation in coloured trees of bounded height.  ...  A current result of Gajarský and Hliněný [9] shows that there exists an FPT algorithm for MSO 2 model checking for graphs of bounded tree-depth, again with elementary dependency on the formula.  ... 
doi:10.1007/978-3-642-32589-2_38 fatcat:ngfzh2gylrdhlbqeqr5fzaci4i

Techniques for Practical Fixed-Parameter Algorithms

F. Huffner, R. Niedermeier, S. Wernicke
2007 Computer journal  
For some of these problems, it can lead to algorithms that are both efficient and yet at the same time guaranteed to find optimal solutions.  ...  The fixed-parameter approach is an algorithm design technique for solving combinatorially hard (mostly NP-hard) problems.  ...  Establishing the FPT of an NP-hard problem thus implies that the combinatorial explosion that is inherent to solving it can be fully confined to the parameter.  ... 
doi:10.1093/comjnl/bxm040 fatcat:jbffitiefzfexftg3lgl7xnsza

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 Algorithms  
We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

Some New Directions and Questions in Parameterized Complexity [chapter]

Rodney G. Downey, Catherine McCartin
2004 Lecture Notes in Computer Science  
In this paper, we will report on some of these, concentrating on some open questions, and also looking at some of our ideas towards applying ideas of parametric complexity in the field of online model  ...  Recently there have been some new initiatives in the field of parameterized complexity.  ...  Recently the increased computational power available has shown that there are a lot of problems for which exponentail time algorithms can be useful in practice.  ... 
doi:10.1007/978-3-540-30550-7_2 fatcat:svswlh6hzrb23gpr7rzmk4shda
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