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Constant Factor Approximation for Subset Feedback Set Problems via a new LP relaxation

2015
*
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
*

One reason

doi:10.1137/1.9781611974331.ch58
dblp:conf/soda/ChekuriM16a
fatcat:ukdjgibwfrg77bpeyjeswyaala
*for*the difficulty in addressing*feedback**set**problems*in undirected graphs has been the lack of*LP**relaxations*with*constant**factor*integrality gaps; the natural*LP*has an integrality gap of ... In this paper, we introduce*new**LP**relaxations**for**Subset*-FES and*Subset*-FVS and show that their integrality gap is at most 13. ... Recall that*Subset*-FVS captures Node-wt-MC as*a*special case and all the known*constant**factor**approximations**for*Node-wt-MC are*via**LP**relaxations*. ...##
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New algorithms for maximum disjoint paths based on tree-likeness

2017
*
Mathematical programming
*

We provide

doi:10.1007/s10107-017-1199-3
pmid:30956356
pmcid:PMC6417437
fatcat:roghxdlfbbggxa4i25jzct6vlq
*new*bounds formulated in terms of the*feedback*vertex*set*number r of*a*graph, which measures its vertex deletion distance to*a*forest. ... We study the classical NP -hard*problems*of finding maximum-size*subsets*from given*sets*of k terminal pairs that can be routed*via*edge-disjoint paths (MaxEDP) or node-disjoint paths (MaxNDP) in*a*given ...*For*planar graphs, there is*a**constant*-*factor**approximation*algorithm with congestion 2 [42] . ...##
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New Algorithms for Maximum Disjoint Paths Based on Tree-Likeness
[article]

2016
*
arXiv
*
pre-print

We study the classical NP-hard

arXiv:1603.01740v2
fatcat:t6f6bgaxpjbtxdngc2z4zdj7zi
*problems*of finding maximum-size*subsets*from given*sets*of k terminal pairs that can be routed*via*edge-disjoint paths (MaxEDP) or node-disjoint paths (MaxNDP) in*a*given ... We provide*new*bounds formulated in terms of the*feedback*vertex*set*number r of*a*graph, which measures its vertex deletion distance to*a*forest. ...*For*planar graphs, there is*a**constant*-*factor**approximation*algorithm with congestion 2 [42] . Very recently, Chuzhoy et al. ...##
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Half-integrality, LP-branching and FPT Algorithms
[chapter]

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

Examples of

doi:10.1137/1.9781611973402.128
dblp:conf/soda/Wahlstrom14
fatcat:73y5sdxakrdbnng7xblchtyk5u
*LP*-*relaxations*which are 2-*approximate*but not half-integral would include Multicut in Trees [22] and*Feedback*Vertex*Set*[12]; see also results achieved*via*iterative rounding [32, 20] , e.g ... The latter result also implies the first singleexponential time FPT algorithm*for**Subset**Feedback*Vertex*Set*, answering an open question of Cygan et al. (2012) . ... Acknowledgements The second author thanks Marek Cygan, Andreas Karrenbauer, Johan Thapper and StanislavŽivný*for*enlightening discussions. ...##
###
The Generalized Deadlock Resolution Problem
[chapter]

2005
*
Lecture Notes in Computer Science
*

This

doi:10.1007/11523468_69
fatcat:7bf62puakva35jcxyof3aykzqy
*problem*also turns out be*a*natural generalization of the directed*feedback*vertex*set**problem*. ... In this paper we initiate the study of the AND-OR directed*feedback*vertex*set**problem*from the viewpoint of*approximation*algorithms. ... Acknowledgement We would like to thank, Ondrej Such,*a*developer at Microsoft*for*asking his question on the Algorithm's email list. ...##
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Half-integrality, LP-branching and FPT Algorithms
[article]

2014
*
arXiv
*
pre-print

Taking

arXiv:1310.2841v2
fatcat:wrwnsr6evrdufe7h7gtqs62avu
*a*slightly different approach, we view half-integrality as*a*discrete*relaxation*of*a**problem*, e.g.,*a**relaxation*of the search space from {0,1}^V to {0,1/2,1}^V such that the*new**problem*admits ... The latter result also implies the first single-exponential time FPT algorithm*for**Subset**Feedback*Vertex*Set*, answering an open question of Cygan et al. (2012). ... Acknowledgements The second author thanks Marek Cygan, Andreas Karrenbauer, Johan Thapper and StanislavŽivný*for*enlightening discussions. ...##
###
Half-integrality, LP-branching, and FPT Algorithms

2016
*
SIAM journal on computing (Print)
*

Taking

doi:10.1137/140962838
fatcat:h4xvlh7kjzcl7l7z464psrayi4
*a*slightly different approach, we view half-integrality as*a*discrete*relaxation*of*a**problem*, e.g.,*a**relaxation*of the search space from {0, 1} V to {0, 1 /2, 1} V such that the*new**problem*admits ... The latter result also implies the first single-exponential time FPT algorithm*for**Subset**Feedback*Vertex*Set*, answering an open question of Cygan et al. (2012) . ... The second author thanks Marek Cygan, Andreas Karrenbauer, Johan Thapper and StanislavŽivný*for*enlightening discussions. ...##
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Algorithms for 2-Route Cut Problems
[chapter]

2008
*
Lecture Notes in Computer Science
*

In the

doi:10.1007/978-3-540-70575-8_39
fatcat:mv3i2qrrr5ejvlfd6o7kkelstq
*subset**feedback**problem*,*a**set*of terminals S ⊆ V defines C;*a*cycle C ∈ C iff C contains*a*terminal. An O(1)*approximation*is known*for*this*problem*even in the node-weighted*setting*[14] . ... In undirected graphs,*a*2route cuts*for*node-disjoint paths give rise to*new*and interesting*feedback**problems*, e.g., the 2-route multiway-cut*problem*corresponds to the*feedback**problem*where C is the ... Acknowledgments: We thank anonymous reviewers*for*detailed and useful comments on previous versions of this paper. ...##
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Multiway cuts in node weighted graphs

2004
*
Journal of Algorithms
*

Comput. 23 (4) (1994) 864-894)

doi:10.1016/s0196-6774(03)00111-1
fatcat:jxfpih7nezhebbrj5q7p2bcxzq
*for*the edge version of this*problem*. This is done by showing that the associated*LP*-*relaxation*always has*a*half-integral optimal solution. ...*A*(2 -2/k)*approximation*algorithm is presented*for*the node multiway cut*problem*, thus matching the result of Dahlhaus et al. (SIAM J. ... Finally,*a*common generalization of the node multiway cut*problem*and the*feedback*node*set**problem*, called the*subset**feedback*vertex*set**problem*was studied recently in [6] , and*a**factor*8*approximation*...##
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Improved Approximation for Node-Disjoint Paths in Grids with Sources on the Boundary

2018
*
International Colloquium on Automata, Languages and Programming
*

In

doi:10.4230/lipics.icalp.2018.38
dblp:conf/icalp/ChuzhoyKN18
fatcat:l2y7nkzcb5bivlrcvz5ez3e22u
*a*very recent follow-up work, the authors further show that NDP in grid graphs is hard to*approximate*to within*factor*Ω(2 log 1− n )*for*any*constant*under standard complexity assumptions, and to within ... The best current*approximation**for*the*problem*is achieved by*a*simple greedy O( √ n)-*approximation*algorithm. ... We write an*LP*-*relaxation**for*this*problem*and design*a*2 O( √ log n•log log n) -*approximation**LP*-rounding algorithm*for*it. ...##
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Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards

2007
*
Foundations of Computer Science (FOCS), IEEE Annual Symposium on
*

We design

doi:10.1109/focs.2007.4389518
fatcat:7vwgowenfvhxvibkzqp37zs3kq
*a**constant**factor**approximation*to the*FEEDBACK*MAB*problem*by solving and rounding*a*natural*LP**relaxation*to this*problem*. ... As far as we are aware, this is the first*approximation*algorithm*for**a*POMDP*problem*. ... Acknowledgment: We thank Ashish Goel and Saswati Sarkar*for*several helpful discussions. ...##
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Simple and Fast Rounding Algorithms for Directed and Node-weighted Multiway Cut

2015
*
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
*

DIR-MC admits

doi:10.1137/1.9781611974331.ch57
dblp:conf/soda/ChekuriM16
fatcat:5gkbcpxgvravjhkfe2xa6q5q7e
*a*2-*approximation*[28] and NODE-WT-MC admits*a*2(1 − 1 k )*approximation*[21], both*via*rounding of*LP**relaxations*. ... In this paper we describe extremely simple and near linear-time rounding algorithms*for*DIR-MC and NODE-WT-MC*via**a*natural distance based*LP**relaxation*. ... CC also thanks Anupam Gupta*for*discussion on some of the*problems*considered in [9] during an Oberwolfach workshop. ...##
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Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards

2007
*
48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)
*

We design

doi:10.1109/focs.2007.23
dblp:conf/focs/Cheng07
fatcat:ilsxlf65vncfrigejrfkofgxbi
*a**constant**factor**approximation*to the*FEEDBACK*MAB*problem*by solving and rounding*a*natural*LP**relaxation*to this*problem*. ... As far as we are aware, this is the first*approximation*algorithm*for**a*POMDP*problem*. ... Acknowledgment: We thank Ashish Goel and Saswati Sarkar*for*several helpful discussions. ...##
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LP-branching algorithms based on biased graphs
[article]

2020
*
arXiv
*
pre-print

This framework captures many of the

arXiv:1610.06060v2
fatcat:2mw2we5tavdo7itrveuuvk7oru
*problems*previously solved*via*the VCSP approach to*LP*-branching, as well as*new*generalisations, such as Group*Feedback*Vertex*Set**for*infinite groups (e.g.,*for*graphs ... We give*a*combinatorial condition*for*the existence of efficient,*LP*-based FPT algorithms*for**a*broad class of graph-theoretical optimisation*problems*. ... Using this connection, FPT LPbranching algorithms were provided that significantly improved the running times*for**a*range of*problems*, including*Subset**Feedback*Vertex*Set*and Group*Feedback*Vertex*Set*...##
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Approximating the two-level facility location problem via a quasi-greedy approach

2006
*
Mathematical programming
*

This is the first non-trivial

doi:10.1007/s10107-006-0704-x
fatcat:ntg5uh3ldnhtlfw4rny6s4zhqa
*approximation**for**a*non-metric multi-level facility location*problem*. ... We propose*a*quasi-greedy algorithm*for**approximating*the classical uncapacitated 2-level facility location*problem*(2-LFLP). ... The author would like to thank Yinyu Ye*for*his support and his*feedbacks*on preliminary drafts of this paper. ...
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