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On Multiway Cut parameterized above lower bounds
[article]

2011
*
arXiv
*
pre-print

Our results imply O*(4^k)

arXiv:1107.1585v1
fatcat:b757pc4i4bdqtftsas3pjiuebq
*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] . ...##
###
Directed Multicut with linearly ordered terminals
[article]

2014
*
arXiv
*
pre-print

We show that this

arXiv:1407.7498v1
fatcat:bafitu7lr5fxbkocpcvu3qt3cy
*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. ...##
###
Faster Exact Algorithms for Some Terminal Set Problems
[chapter]

2013
*
Lecture Notes in Computer Science
*

Our

doi:10.1007/978-3-319-03898-8_14
fatcat:3vtcab26sjemfhrludpfe4jzia
*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*. ...##
###
Faster exact algorithms for some terminal set problems

2017
*
Journal of computer and system sciences (Print)
*

We call this class of

doi:10.1016/j.jcss.2017.04.003
fatcat:72vr6rvmrzep3oka25jbxzupsm
*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*. ...##
###
Efficient Enumerations for Minimal Multicuts and Multiway Cuts

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. ...

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

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). ...

##
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Hypergraph Cuts with General Splitting Functions
[article]

2020
*
arXiv
*
pre-print

We also analyze extensions to

arXiv:2001.02817v1
fatcat:tfjnelvk5ngrxalvxdbenhw2by
*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. ...##
###
Quick Separation in Chordal and Split Graphs

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*. ...

##
###
Parameterized Complexity of DAG Partitioning
[chapter]

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,

doi:10.1007/978-3-642-38233-8_5
fatcat:synxwc53xrhxhclewowtegeesa
*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. ...##
###
Linear-Time FPT Algorithms via Network Flow
[chapter]

2013
*
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
*

In

doi:10.1137/1.9781611973402.127
dblp:conf/soda/IwataOY14
fatcat:bb3c7zuo6jhxfpsmxrpbloyoya
*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*. ...##
###
Linear-Time FPT Algorithms via Network Flow
[article]

2013
*
arXiv
*
pre-print

In

arXiv:1307.4927v1
fatcat:fvncxo7qzzc5holl7mcmli44ru
*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*. ...##
###
An O⁎(1.84k) parameterized algorithm for the multiterminal cut problem

2014
*
Information Processing Letters
*

We study

doi:10.1016/j.ipl.2013.12.001
fatcat:bnwg3srpqjctzdppjyhm7pibui
*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. ...##
###
Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset
[chapter]

2012
*
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
*

Given a directed graph G, a set of k terminals, and

doi:10.1137/1.9781611973099.136
dblp:conf/soda/ChitnisHM12
fatcat:rjqvaf5k2neyxoqc4f427ghkey
*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*. ...##
###
Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset

2013
*
SIAM journal on computing (Print)
*

Given a directed graph G, a set of k terminals, and

doi:10.1137/12086217x
fatcat:ivxfnobzujcsbdxsoqs4n4omce
*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*. ...##
###
Parameterized Algorithms for Zero Extension and Metric Labelling Problems

2018
*
International Colloquium on Automata, Languages and Programming
*

Depending on

doi:10.4230/lipics.icalp.2018.94
dblp:conf/icalp/ReidlW18
fatcat:4jmgw2vhdvejbey2l47dkfml4a
*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. ...
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