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

Chandra Chekuri, Vivek Madan
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
One reason 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.  ... 
doi:10.1137/1.9781611974331.ch58 dblp:conf/soda/ChekuriM16a fatcat:ukdjgibwfrg77bpeyjeswyaala

New algorithms for maximum disjoint paths based on tree-likeness

Krzysztof Fleszar, Matthias Mnich, Joachim Spoerhase
2017 Mathematical programming  
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.  ...  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] .  ... 
doi:10.1007/s10107-017-1199-3 pmid:30956356 pmcid:PMC6417437 fatcat:roghxdlfbbggxa4i25jzct6vlq

New Algorithms for Maximum Disjoint Paths Based on Tree-Likeness [article]

Krzysztof Fleszar and Matthias Mnich and Joachim Spoerhase
2016 arXiv   pre-print
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  ...  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.  ... 
arXiv:1603.01740v2 fatcat:t6f6bgaxpjbtxdngc2z4zdj7zi

Half-integrality, LP-branching and FPT Algorithms [chapter]

Magnus Wahlström
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
Examples of 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.  ... 
doi:10.1137/1.9781611973402.128 dblp:conf/soda/Wahlstrom14 fatcat:73y5sdxakrdbnng7xblchtyk5u

The Generalized Deadlock Resolution Problem [chapter]

Kamal Jain, MohammadTaghi Hajiaghayi, Kunal Talwar
2005 Lecture Notes in Computer Science  
This 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.  ... 
doi:10.1007/11523468_69 fatcat:7bf62puakva35jcxyof3aykzqy

Half-integrality, LP-branching and FPT Algorithms [article]

Yoichi Iwata and Magnus Wahlström and Yuichi Yoshida
2014 arXiv   pre-print
Taking 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.  ... 
arXiv:1310.2841v2 fatcat:wrwnsr6evrdufe7h7gtqs62avu

Half-integrality, LP-branching, and FPT Algorithms

Yoichi Iwata, Magnus Wahlström, Yuichi Yoshida
2016 SIAM journal on computing (Print)  
Taking 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.  ... 
doi:10.1137/140962838 fatcat:h4xvlh7kjzcl7l7z464psrayi4

Algorithms for 2-Route Cut Problems [chapter]

Chandra Chekuri, Sanjeev Khanna
2008 Lecture Notes in Computer Science  
In the 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.  ... 
doi:10.1007/978-3-540-70575-8_39 fatcat:mv3i2qrrr5ejvlfd6o7kkelstq

Multiway cuts in node weighted graphs

Naveen Garg, Vijay V. Vazirani, Mihalis Yannakakis
2004 Journal of Algorithms  
Comput. 23 (4) (1994) 864-894) 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  ... 
doi:10.1016/s0196-6774(03)00111-1 fatcat:jxfpih7nezhebbrj5q7p2bcxzq

Improved Approximation for Node-Disjoint Paths in Grids with Sources on the Boundary

Julia Chuzhoy, David H. K. Kim, Rachit Nimavat, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
In 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.  ... 
doi:10.4230/lipics.icalp.2018.38 dblp:conf/icalp/ChuzhoyKN18 fatcat:l2y7nkzcb5bivlrcvz5ez3e22u

Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards

Sudipto Guha, Kamesh Munagala
2007 Foundations of Computer Science (FOCS), IEEE Annual Symposium on  
We design 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.  ... 
doi:10.1109/focs.2007.4389518 fatcat:7vwgowenfvhxvibkzqp37zs3kq

Simple and Fast Rounding Algorithms for Directed and Node-weighted Multiway Cut

Chandra Chekuri, Vivek Madan
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
DIR-MC admits 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.  ... 
doi:10.1137/1.9781611974331.ch57 dblp:conf/soda/ChekuriM16 fatcat:5gkbcpxgvravjhkfe2xa6q5q7e

Approximation Algorithms for Partial-Information Based Stochastic Control with Markovian Rewards

Sudipto Guha, Kamesh Munagala
2007 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)  
We design 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.  ... 
doi:10.1109/focs.2007.23 dblp:conf/focs/Cheng07 fatcat:ilsxlf65vncfrigejrfkofgxbi

LP-branching algorithms based on biased graphs [article]

Euiwoong Lee, Magnus Wahlström
2020 arXiv   pre-print
This framework captures many of the 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  ... 
arXiv:1610.06060v2 fatcat:2mw2we5tavdo7itrveuuvk7oru

Approximating the two-level facility location problem via a quasi-greedy approach

Jiawei Zhang
2006 Mathematical programming  
This is the first non-trivial 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.  ... 
doi:10.1007/s10107-006-0704-x fatcat:ntg5uh3ldnhtlfw4rny6s4zhqa
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