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Primal-Dual Approximation Algorithms for Feedback Problems in Planar Graphs

Michel X. Goemans, David P. Williamson
1998 Combinatorica  
Our algorithms use the primal-dual method for approximation algorithms as given in Goemans and Williamson 16].  ...  This results in 9 4 -approximation algorithms for the aforementioned feedback and bipartization problems in planar graphs.  ...  Acknowledgements We thank Se Naor for pointing out reference 26], and Jon Kleinberg for helpful discussions.  ... 
doi:10.1007/pl00009810 fatcat:ul5i3yaj4bb7rjuydu73osepui

Primal-dual approximation algorithms for feedback problems in planar graphs [chapter]

Michel X. Goemans, David P. Williamson
1996 Lecture Notes in Computer Science  
This results in ~-approximation algorithms for the aforementioned feedback and bipartization problems in planar graphs.  ...  We give a ]-approxlmation algorithm for the general problem in planar graphs, given that the subset of cycles obeys certain properties.  ...  Acknowledgements We thank Seffi Naor for pointing out reference [22] .  ... 
doi:10.1007/3-540-61310-2_12 fatcat:o3kddqti7jbpxhhwi7y62gn4w4

Primal-Dual Approximation Algorithms for Node-Weighted Steiner Forest on Planar Graphs [chapter]

Carsten Moldenhauer
2011 Lecture Notes in Computer Science  
[DHK09] showed that the generic primal-dual algorithm of Goemans and Williamson [GW97] is a 6-approximation on planar graphs.  ...  Our analysis implies that improving this bound for NODE-WEIGHTED STEINER FOREST via the primal-dual algorithm is essentially as difficult as improving the integrality gap for the feedback problems in [  ...  Further, our work implies strong similarities between the analysis of the primal-dual algorithm for the feedback problems studied in [GW98] and the analysis of the algorithm for NWSF.  ... 
doi:10.1007/978-3-642-22006-7_63 fatcat:gwm7nj2b4fav5eaim7lxtqpsuu

Primal-Dual Approximation Algorithms for Node-Weighted Network Design in Planar Graphs [chapter]

Piotr Berman, Grigory Yaroslavtsev
2012 Lecture Notes in Computer Science  
We present primal-dual algorithms which give a 2.4 approximation for a class of node-weighted network design problems in planar graphs, introduced by Demaine, Hajiaghayi and Klein (ICALP'09).  ...  In contrast, for more general node-weighted versions constant factor approximations via primal-dual algorithms remain the state of the art, while no APX-hardness is known.  ...  Experimental evaluation of primal-dual algorithms for feedback vertex set problems in planar graphs in applications to VLSI design was shown by Kahng, Vaya and Zelikovsky [20] .  ... 
doi:10.1007/978-3-642-32512-0_5 fatcat:3g2lfstnd5ehdgzemr3wzk7fcy

Page 1321 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
This results in 3- approximation algorithms for the aforementioned feedback and bipartization problems in planar graphs.  ...  Our algorithms use the primal-dual method for approximation algorithms as given in our forthcoming paper [“The primal-dual method for approximation algorithms and its application to network design problems  ... 

The primal-dual method for approximation algorithms

David P. Williamson
2002 Mathematical programming  
Because of parallels with the primal-dual method commonly used in combinatorial optimization, we call it the primal-dual method for approximation algorithms.  ...  We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems  ...  The author would like to thank Tim Roughgarden, David Shmoys, Madhu Sudan, and the two anonymous referees for several comments that improved the presentation of this survey.  ... 
doi:10.1007/s101070100262 fatcat:onefvz77yvh5vfpgb2zjl6qr3e

Page 1587 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
problems in planar graphs.  ...  Brown (1-ILCC-MS; Chicago, IL) 2000b:90106 90C35 05C85 68R10 Goemans, Michel X. (1-MIT; Cambridge, MA); Williamson, David P. (1-IBM; Yorktown Heights, NY) Primal-dual approximation algorithms for feedback  ... 

A primal–dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs

Fabián A. Chudak, Michel X. Goemans, Dorit S. Hochbaum, David P. Williamson
1998 Operations Research Letters  
We show how their algorithms can be explained in terms of the primal-dual method for approximation algorithms, which has been used to derive approximation algorithms for network design problems.  ...  Recently, Becker and Geiger and Bafna, Berman and Fujito gave 2-approximation algorithms for the feedback vertex set problem in undirected graphs.  ...  Acknowledgements We thank David Shmoys for several useful conversations.  ... 
doi:10.1016/s0167-6377(98)00021-2 fatcat:lzekbcpn45eq3d5fysgrczumqe

Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs [article]

Chandra Chekuri and Alina Ene and Ali Vakilian
2019 arXiv   pre-print
in planar graphs and proper minor-closed families of graphs via a primal-dual algorithm.  ...  Our main result is an O(k)-approximation algorithm for EC-SNDP and Elem-SNDP when the input graph is planar or more generally if it belongs to a proper minor-closed family of graphs; here k=max_uv r(uv  ...  The analysis of the primal-dual algorithm that we present is probably not tight and it would be interesting to obtain the tightest bound one can prove for the algorithm.  ... 
arXiv:1910.07616v1 fatcat:d4rzlpmv5nhgjkd5rjkoo66gq4

A primal-dual approach to approximation of node-deletion problems for matroidal properties [chapter]

Toshihiro Fujito
1997 Lecture Notes in Computer Science  
A primal{ dual approximation algorithm based on this and the dual of its linear relaxation is then presented.  ...  ) problem in undirected graphs.  ...  Chudak et al. gave new primal{dual formulations and the algorithms based on them for the FVS problem in undirected graphs [CGHW96] .  ... 
doi:10.1007/3-540-63165-8_228 fatcat:ztnm5wplxfbajefrmrw4zaspfq

Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference

Reuven Bar-Yehuda, Dan Geiger, Joseph (Seffi) Naor, Ron M. Roth
1998 SIAM journal on computing (Print)  
Given an undirected graph G with n vertices and weights on its vertices, polynomial-time algorithms are provided for approximating the problem of nding a feedback vertex set of G with a smallest weight  ...  For general vertex weights, the performance ratio becomes minf2 2 4 log 2 ng where denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10.  ...  Acknowledgment We would like to thank David Johnson for bringing EP62] to our attention, and Samir Khuller for helpful discussions.  ... 
doi:10.1137/s0097539796305109 fatcat:rrc446nc4bee5g4wchm46frtoa

A Constant-factor Approximation for Weighted Bond Cover [article]

Eun Jung Kim and Euiwoong Lee and Dimitrios M. Thilikos
2021 arXiv   pre-print
We study the problem for the class F of θ_c-minor-free graphs, under the equivalent setting of the Weighted c-Bond Cover problem, and present a constant-factor approximation algorithm using the primal-dual  ...  Besides making an important step in the quest of (dis)proving a constant-factor approximation for Weighted ℱ-Vertex Deletion, our result may be useful as a template for algorithms for other minor-closed  ...  Feedback Vertex Set, 2-approximation algorithms were proposed using the primal-dual method [7, 13, 19] .  ... 
arXiv:2105.00857v1 fatcat:gvai3sfc2bcvrewuajt2ckqtg4

Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

Jeff Erickson, Philip N. Klein, Dániel Marx, Claire Mathieu, Marc Herbstritt
2016 Dagstuhl Reports  
This report contains abstracts for the recent developments in planar graph algorithms discussed during the seminar as well as summaries of open problems in this area of research.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 16221 "Algorithms for Optimization Problems in Planar Graphs". The seminar was held from May 29 to June 3, 2016.  ...  In addition, we obtain a polynomial-time approximation scheme for feedback vertex set in planar graphs.  ... 
doi:10.4230/dagrep.6.5.94 dblp:journals/dagstuhl-reports/EricksonKMM16 fatcat:wasdfgivt5fqdppfxo3iqqs2ta

A Linear-Time Approximation Scheme for TSP in Undirected Planar Graphs with Edge-Weights

Philip N. Klein
2008 SIAM journal on computing (Print)  
We give an algorithm requiring O(c 1/ǫ 2 n) time to find an ǫ-optimal traveling salesman tour in the shortest-path metric defined by an undirected planar graph with nonnegative edgelengths.  ...  For the case of all lengths equal to 1, the time required is O(c 1/ǫ n).  ...  Thanks also to Glencora Borradaile and Erik Demaine for helpful discussions and suggestions.  ... 
doi:10.1137/060649562 fatcat:qkvmtagkdvgrbobjn2zi2fgsku

Combinatorial algorithms for feedback problems in directed graphs

Camil Demetrescu, Irene Finocchi
2003 Information Processing Letters  
We present simple combinatorial algorithms for these problems that achieve an approximation ratio bounded by the length, in terms of number of arcs, of a longest simple cycle of the digraph.  ...  Given a weighted directed graph G = (V, A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A ⊆ A such that the directed graph (V, A\A ) is acyclic.  ...  In this paper we focus on feedback problems on directed graphs and we present new approximation algorithms for them built on the top of the local-ratio technique [2] .  ... 
doi:10.1016/s0020-0190(02)00491-x fatcat:6hczz3tgo5f6tolcu4ge7c5rry
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