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Branch-and-Reduce Exponential/FPT Algorithms in Practice: A Case Study of Vertex Cover [article]

Takuya Akiba, Yoichi Iwata
2014 arXiv   pre-print
In this paper, we design a branch-and-reduce algorithm for the vertex cover problem using the techniques developed for theoretical algorithms and compare its practical performance with other state-of-the-art  ...  We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems.  ...  The authors are supported by Grant-in-Aid for JSPS Fellows 256563 and 256487.  ... 
arXiv:1411.2680v1 fatcat:mdyxwas46fexndrm5fci5qcsly

Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover

Takuya Akiba, Yoichi Iwata
2016 Theoretical Computer Science  
In this paper, we design a branch-and-reduce algorithm for the vertex cover problem using the techniques developed for theoretical algorithms and compare its practical performance with other stateof-the-art  ...  We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems.  ...  In this paper, we study the practical impact of theoretical research on branching algorithms.  ... 
doi:10.1016/j.tcs.2015.09.023 fatcat:a6smbwafebcuffwuuynk4bkmcm

Branch-and-Reduce Exponential/FPT Algorithms in Practice: A Case Study of Vertex Cover [chapter]

Takuya Akiba, Yoichi Iwata
2014 2015 Proceedings of the Seventeenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
In this paper, we design a branch-and-reduce algorithm for the vertex cover problem using the techniques developed for theoretical algorithms and compare its practical performance with other state-of-the-art  ...  Let us consider a very simple algorithm that selects a vertex v and branches into two cases: either 1) including v to the vertex cover or 2) discarding v while including its neighbors to the vertex cover  ...  The authors are supported by Grant-in-Aid for JSPS Fellows 256563 and 256487.  ... 
doi:10.1137/1.9781611973754.7 dblp:conf/alenex/AkibaI15 fatcat:gdn72zraezb4vgok77s5rssd5y

A Single-Exponential FPT Algorithm for the K 4-Minor Cover Problem [chapter]

Eun Jung Kim, Christophe Paul, Geevarghese Philip
2012 Lecture Notes in Computer Science  
While a single-exponential FPT algorithm has been known for a long time for Vertex Cover, such an algorithm for Feedback Vertex Set was devised comparatively recently.  ...  in a graph of treewidth at most 2.  ...  We would like to thank Saket Saurabh for his insightful comments on an early draft and Stefan Szeider for pointing out the application of our problem in Bayesian Networks.  ... 
doi:10.1007/978-3-642-31155-0_11 fatcat:gqnrcyxuvnbzdk32fujb3bguna

A single-exponential FPT algorithm for the K_4-minor cover problem [article]

Eun Jung Kim and Christophe Paul and Geevarghese Philip
2012 arXiv   pre-print
While a single-exponential FPT algorithm has been known for a long time for Vertex Cover, such an algorithm for Feedback Vertex Set was devised comparatively recently.  ...  in a graph of treewidth at most 2.  ...  We would like to thank Saket Saurabh for his insightful comments on an early draft and Stefan Szeider for pointing out the application of our problem in Bayesian Networks.  ... 
arXiv:1204.1417v1 fatcat:3ygho6u2pzfihezc6tnq5cieva

Parameterized algorithms of fundamental NP-hard problems: a survey

Wenjun Li, Yang Ding, Yongjie Yang, R. Simon Sherratt, Jong Hyuk Park, Jin Wang
2020 Human-Centric Computing and Information Sciences  
, Feedback Vertex Set, Hyperplane Cover, Vertex Cover, Packing and Matching problems.  ...  In this paper, we are focused on the algorithms' main idea and algorithmic techniques, and omit the details of them.  ...  Acknowledgements The authors would like to thank the reviewers for their valuable comments which improve the quality of this paper dramatically.  ... 
doi:10.1186/s13673-020-00226-w fatcat:2ncywbdlnrdtzliiz4tyi76df4

Finding Highly Connected Subgraphs [chapter]

Falk Hüffner, Christian Komusiewicz, Manuel Sorge
2015 Lecture Notes in Computer Science  
Thus, we explore possible parameterizations, such as the solution size, number of vertices in the input, the size of a vertex cover in the input, and the number of edges outgoing from the solution (edge  ...  If we take the minimum size of a vertex cover τ for G as parameter, we obtain the first fixed-parameter algorithm: the problem can be solved in O((2τ ) τ · n O(1) ) time (Corollary 1).  ...  Edge Isolation Parameter We now present a single-exponential FPT algorithm for the number γ of edges between the desired highly connected subgraph G[S] and the remaining graph.  ... 
doi:10.1007/978-3-662-46078-8_21 fatcat:z73kwetemzgl5atrtyhds2rxri

There and Back Again: On Applying Data Reduction Rules by Undoing Others [article]

Aleksander Figiel and Vincent Froese and André Nichterlein and Rolf Niedermeier
2022 arXiv   pre-print
In particular, based on the example of Vertex Cover we propose two methods applying backward rules to shrink the instances further.  ...  A data reduction rule is a polynomial-time algorithm that, given a problem instance as input, outputs an equivalent, typically smaller instance of the same problem.  ...  Branch-and-reduce exponential/fpt algorithms in practice: A case study of vertex cover. Theoretical Computer Science, 609:211-225, 2016. doi: 10.1016/j.tcs.2015.09.023.  ... 
arXiv:2206.14698v1 fatcat:xrloszt72zaudhfhekifggxegy

Kernelization for Treewidth-2 Vertex Deletion [article]

Jeroen L.G. Schols
2022 arXiv   pre-print
To develop a constructive kernelization algorithm, we present a new method to decompose graphs into near-protrusions, such that near-protrusions in this new decomposition can be reduced using elementary  ...  ., a preprocessing routine that in polynomial time outputs an equivalent instance of size t^O(1).  ...  [34] introduced the first single-exponential FPT algorithm for the {K 4 }-Minor Cover problem parameterized by target size.  ... 
arXiv:2203.10070v1 fatcat:wwgdzrskpzfypaijleupjv7eo4

Algorithm Engineering for Cut Problems [article]

Alexander Noe
2021 arXiv   pre-print
All of these algorithms are efficient in practice and freely available for use.  ...  In this work, we aim to partition the vertices of a graph into multiple blocks while minimizing the number of edges that connect different blocks.  ...  [27] “Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover”. In: Theor. Comput. Sci. 609, Part 1 (2016), pp. 211–225. [28] R. Brillout.  ... 
arXiv:2108.04566v1 fatcat:4tpyybkhsvg6toiuxkvdvychqu

Makespan Scheduling of Unit Jobs with Precedence Constraints in O(1.995^n) time [article]

Jesper Nederlof, Céline M. F. Swennenhuis, Karol Węgrzycki
2022 arXiv   pre-print
A crucial ingredient of our approach is an algorithm with a runtime that is only single-exponential in the vertex cover of the comparability graph of the precedence constraint graph.  ...  In a classical scheduling problem, we are given a set of n jobs of unit length along with precedence constraints and the goal is to find a schedule of these jobs on m identical machines that minimizes  ...  We are thankful for the possibility of working in the stimulating and creative research environment at HIM. We also thank Adam Polak for useful discussions.  ... 
arXiv:2208.02664v1 fatcat:eezcejx5wzhefijzppb7xr4nkq

Lossy Planarization: A Constant-Factor Approximate Kernelization for Planar Vertex Deletion [article]

Bart M. P. Jansen, Michał Włodarczyk
2022 arXiv   pre-print
In this work we show that Vertex planarization admits an algorithm which is a combination of both approaches.  ...  The Vertex planarization problem is a special case of F-minor-free deletion for the family F = K_5, K_3,3.  ...  , a randomized constant-factor approximation algorithm, and a single-exponential FPT algorithm.  ... 
arXiv:2202.02174v1 fatcat:56qsslym3nbkxlmrbacnobhbdm

Exploring the complexity of layout parameters in tournaments and semi-complete digraphs [article]

Florian Barbero, Christophe Paul, Michał Pilipczuk
2017 arXiv   pre-print
We study the complexity of computing two layout parameters of semi-complete digraphs: cutwidth and optimal linear arrangement (OLA).  ...  A simple digraph is semi-complete if for any two of its vertices u and v, at least one of the arcs (u,v) and (v,u) is present.  ...  By applying a standard branching strategy, we obtain a single-exponential FPT algorithm for c-Cutwidth Vertex Deletion in semi-complete digraphs. Proof. Let D be the input digraph.  ... 
arXiv:1706.00617v1 fatcat:7aoy6ah4znbbzc6u77xckl2hwe

Targeted Branching for the Maximum Independent Set Problem

Demian Hespe, Sebastian Lamm, Christian Schorr
2021
In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms.  ...  In this work, we develop and evaluate several novel branching strategies for both branch-andbound and branch-and-reduce algorithms.  ...  References 1 Takuya Akiba and Yoichi Iwata. Branch-and-reduce exponential/FPT algorithms in practice: A case study of vertex cover.  ... 
doi:10.5445/ir/1000134359 fatcat:gbej22ykyjf6tonwhxp4e5nqcu

On the Parameterized Complexity of Polytree Learning

Niels Grüttemeier, Christian Komusiewicz, Nils Morawietz
2021 Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence   unpublished
In this work, we revisit the complexity of Polytree Learning. We show that Polytree Learning can be solved in single-exponential FPT time for the number of variables.  ...  Finally, we show that if d and the maximum parent set size are bounded, then we can obtain efficient algorithms.  ...  One of the earliest special cases that has received attention are tree networks, also called branchings. A tree is a Bayesian network where every vertex has at most one parent.  ... 
doi:10.24963/ijcai.2021/580 fatcat:wm423pg6wfezbdinz7gi76wofu
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