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On Multiway Cut parameterized above lower bounds [article]

Marek Cygan, Marcin Pilipczuk, Michał Pilipczuk, Jakub Onufry Wojtaszczyk
2011 arXiv   pre-print
Our results imply O*(4^k) algorithms for Vertex Cover above Maximum Matching and Almost 2-SAT as well as an O*(2^k) algorithm for Node Multiway Cut with a standard parameterization by the solution size  ...  In this paper we consider two above lower bound parameterizations of the Node Multiway Cut problem - above the maximum separating cut and above a natural LP-relaxation - and prove them to be fixed-parameter  ...  Acknowledgements We thank Saket Saurabh for pointing us to [9] .  ... 
arXiv:1107.1585v1 fatcat:b757pc4i4bdqtftsas3pjiuebq

Directed Multicut with linearly ordered terminals [article]

Robert F. Erbacher, Trent Jaeger, Nirupama Talele, Jason Teutsch
2014 arXiv   pre-print
We show that this problem is fixed-parameter tractable when parametrized in the cutset size p via an algorithm running in O(4^p p n^4) time.  ...  What is the size of the smallest edge cut which eliminates all paths from t_i to t_j for all i < j?  ...  Let G be an undirected graph with terminal nodes s, t and u be an instance of Multiway Cut, the problem of finding a smallest edge cut which separates s, t, and u.  ... 
arXiv:1407.7498v1 fatcat:bafitu7lr5fxbkocpcvu3qt3cy

Faster Exact Algorithms for Some Terminal Set Problems [chapter]

Rajesh Chitnis, Fedor V. Fomin, Daniel Lokshtanov, Pranabendu Misra, M. S. Ramanujan, Saket Saurabh
2013 Lecture Notes in Computer Science  
Our algorithms for Node Multiway Cut, and Subset Feedback Vertex Set on chordal graphs improve the current best algorithms for these problems and answers an open question posed in [15] .  ...  Furthermore, our algorithms for Directed Unrestricted Node Multiway Cut and Directed Subset Feedback Vertex Set are the first exact algorithms improving upon the brute force O * (2 n )-algorithms.  ...  Node Multiway Cut In this subsection, we give an exact algorithm for the Node Multiway Cut problem.  ... 
doi:10.1007/978-3-319-03898-8_14 fatcat:3vtcab26sjemfhrludpfe4jzia

Faster exact algorithms for some terminal set problems

Rajesh Chitnis, Fedor V. Fomin, Daniel Lokshtanov, Pranabendu Misra, M.S. Ramanujan, Saket Saurabh
2017 Journal of computer and system sciences (Print)  
We call this class of problems as terminal set problems. In this paper we introduce a general method to obtain faster exact exponential time algorithms for many terminal set problems.  ...  Many problems on graphs can be expressed in the following language: given a graph G = (V, E) and a terminal set T ⊆ V , find a minimum size set S ⊆ V which intersects all "structures" (such as cycles or  ...  Node Multiway Cut In this subsection, we give an exact algorithm for the Node Multiway Cut problem.  ... 
doi:10.1016/j.jcss.2017.04.003 fatcat:72vr6rvmrzep3oka25jbxzupsm

Efficient Enumerations for Minimal Multicuts and Multiway Cuts

Kazuhiro Kurita, Yasuaki Kobayashi, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
algorithm for minimal edge multiway cuts.  ...  We improve the running time bound for this special case: We devise a polynomial delay and exponential space enumeration algorithm for minimal node multiway cuts and a polynomial delay and space enumeration  ...  For the problem of enumerating minimal Steiner edge multicuts, we could neither develop an efficient algorithm nor prove some correspondence as in Lemma 29. We leave this question for future work.  ... 
doi:10.4230/lipics.mfcs.2020.60 dblp:conf/mfcs/KuritaK20 fatcat:4lc42joti5fofiqlzoq6vsthty

Multi-Multiway Cut Problem on Graphs of Bounded Branch Width [chapter]

Xiaojie Deng, Bingkai Lin, Chihao Zhang
2013 Lecture Notes in Computer Science  
The Multi-Multiway Cut problem proposed by Avidor and Langberg[2] is a natural generalization of Multicut and Multiway Cut problems.  ...  In fact, for fixed c and branch width k, we show that the Multi-Multiway Cut problem can be solved in linear time, thus affirmatively answer the question in [13] .  ...  Acknowledgements The work is supported by NSF of China (61033002) and by Science and Technology Commission of Shanghai Municipality (11XD1402800).  ... 
doi:10.1007/978-3-642-38756-2_32 fatcat:27mum22icrcw7ldbmg5g7gspnu

Hypergraph Cuts with General Splitting Functions [article]

Nate Veldt and Austin R. Benson and Jon Kleinberg
2020 arXiv   pre-print
We also analyze extensions to multiway cuts with at least three terminal nodes and identify a natural class of splitting functions for which the problem can be reduced in an approximation-preserving way  ...  The minimum s-t cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science  ...  The multiway cut problem. The multiway cut problem is a generalization of the undirected minimum s-t cut problem in graphs.  ... 
arXiv:2001.02817v1 fatcat:tfjnelvk5ngrxalvxdbenhw2by

Quick Separation in Chordal and Split Graphs

Pranabendu Misra, Fahad Panolan, Ashutosh Rai, Saket Saurabh, Roohani Sharma, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
An important special case of the Multicut problem is the Multiway Cut problem, where instead of vertex pairs, we are given a set T of terminal vertices, and the goal is to separate every pair of distinct  ...  to construct a polynomial kernel for Multiway Cut.  ...  [5] also gives a 4 k−LP n O(1) time algorithm for Multiway Cut, where LP is the optimal value of the LP relaxation of the natural ILP formulation for the problem.  ... 
doi:10.4230/lipics.mfcs.2020.70 dblp:conf/mfcs/MisraP00S20 fatcat:zvxz7xaj5vairbvhncasrxqze4

Parameterized Complexity of DAG Partitioning [chapter]

René van Bevern, Robert Bredereck, Morgan Chopin, Sepp Hartung, Falk Hüffner, André Nichterlein, Ondřej Suchý
2013 Lecture Notes in Computer Science  
Finally, given a tree decomposition of width w, we show how to solve DAG Partitioning in 2 O(w 2 ) · n time, improving a known algorithm for the parameter pathwidth.  ...  Motivated by NP-hardness and hardness of approximation results, we consider the parameterized complexity of this problem.  ...  Another question is whether there is an algorithm solving the problem in where w is the treewidth, as the O(2 O(w 2 ) · n) running time of our algorithm still seems to limit its practical relevance.  ... 
doi:10.1007/978-3-642-38233-8_5 fatcat:synxwc53xrhxhclewowtegeesa

Linear-Time FPT Algorithms via Network Flow [chapter]

Yoichi Iwata, Keigo Oka, Yuichi Yoshida
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f (k)n  ...  To the best of our knowledge, our algorithms achieve linear time complexity for the first time for these problems.  ...  C A Linear-Time FPT Algorithm for Node Multiway Cut In this section, we give an O(4 k (|V | + |E|))-time FPT algorithm for Node Multiway Cut.  ... 
doi:10.1137/1.9781611973402.127 dblp:conf/soda/IwataOY14 fatcat:bb3c7zuo6jhxfpsmxrpbloyoya

Linear-Time FPT Algorithms via Network Flow [article]

Yoichi Iwata, Keigo Oka, Yuichi Yoshida
2013 arXiv   pre-print
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^  ...  To the best of our knowledge, our algorithms achieve linear time complexity for the first time for these problems.  ...  C A Linear-Time FPT Algorithm for Node Multiway Cut In this section, we give an O(4 k (|V | + |E|))-time FPT algorithm for Node Multiway Cut.  ... 
arXiv:1307.4927v1 fatcat:fvncxo7qzzc5holl7mcmli44ru

An O⁎(1.84k) parameterized algorithm for the multiterminal cut problem

Yixin Cao, Jianer Chen, J.-H. Fan
2014 Information Processing Letters  
We study the multiterminal cut problem, which, given an n-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct  ...  This bounded search tree algorithm can be shown to run in 1.84^k· n^O(1) time, thereby breaking the 2^k· n^O(1) barrier. As a by-product, it gives a 1.36^k· n^O(1) time algorithm for 3-terminal cut.  ...  So we leave it open for a parameterized algorithm for NODE MULTIWAY CUT of time c k · n O(1) for some constant c < 2.  ... 
doi:10.1016/j.ipl.2013.12.001 fatcat:bnwg3srpqjctzdppjyhm7pibui

Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset [chapter]

Rajesh Chitnis, Mohammad Taghi Hajiaghayi, Daniel Marx
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
Given a directed graph G, a set of k terminals, and an integer p, the Directed Vertex Multiway Cut problem asks whether there is a set S of at most p (nonterminal) vertices whose removal disconnects each  ...  Directed Edge Multiway Cut is the analogous problem where S is a set of at most p edges. These two problems are indeed known to be equivalent.  ...  The latter paper improved the randomized sampling process to make the algorithms more efficient; in particular, this improvement results in an O * (2 O(p 2 ) ) algorithm for Directed Multiway Cut.  ... 
doi:10.1137/1.9781611973099.136 dblp:conf/soda/ChitnisHM12 fatcat:rjqvaf5k2neyxoqc4f427ghkey

Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset

Rajesh Chitnis, MohammadTaghi Hajiaghayi, Dániel Marx
2013 SIAM journal on computing (Print)  
Given a directed graph G, a set of k terminals, and an integer p, the Directed Vertex Multiway Cut problem asks whether there is a set S of at most p (nonterminal) vertices whose removal disconnects each  ...  Directed Edge Multiway Cut is the analogous problem where S is a set of at most p edges. These two problems are indeed known to be equivalent.  ...  The latter paper improved the randomized sampling process to make the algorithms more efficient; in particular, this improvement results in an O * (2 O(p 2 ) ) algorithm for Directed Multiway Cut.  ... 
doi:10.1137/12086217x fatcat:ivxfnobzujcsbdxsoqs4n4omce

Parameterized Algorithms for Zero Extension and Metric Labelling Problems

Felix Reidl, Magnus Wahlström, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
Depending on the chosen cost function µ, we find that different algorithmic approaches can be applied to design FPT-algorithms: for arbitrary µ we parameterize by the number of edges that cross the cut  ...  We achieve a similar result for the more general Metric Labelling, while also allowing µ to be the distance metric between an arbitrary subset of nodes in a tree using tools from the theory of VCSPs.  ...  Our algorithm roughly follows the algorithm for Multiway Cut of Chen, Liu and Lu [2] , with two complications.  ... 
doi:10.4230/lipics.icalp.2018.94 dblp:conf/icalp/ReidlW18 fatcat:4jmgw2vhdvejbey2l47dkfml4a
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