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Primal-Dual Approximation Algorithms for Feedback Problems in Planar Graphs

1998
*
Combinatorica
*

Our

doi:10.1007/pl00009810
fatcat:ul5i3yaj4bb7rjuydu73osepui
*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. ...##
###
Primal-dual approximation algorithms for feedback problems in planar graphs
[chapter]

1996
*
Lecture Notes in Computer Science
*

This results

doi:10.1007/3-540-61310-2_12
fatcat:o3kddqti7jbpxhhwi7y62gn4w4
*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] . ...##
###
Primal-Dual Approximation Algorithms for Node-Weighted Steiner Forest on Planar Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

[DHK09] showed that the generic

doi:10.1007/978-3-642-22006-7_63
fatcat:gwm7nj2b4fav5eaim7lxtqpsuu
*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. ...##
###
Primal-Dual Approximation Algorithms for Node-Weighted Network Design in Planar Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-642-32512-0_5
fatcat:3g2lfstnd5ehdgzemr3wzk7fcy
*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] . ...##
###
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

2002
*
Mathematical programming
*

Because of parallels with the

doi:10.1007/s101070100262
fatcat:onefvz77yvh5vfpgb2zjl6qr3e
*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. ...##
###
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

1998
*
Operations Research Letters
*

We show how their

doi:10.1016/s0167-6377(98)00021-2
fatcat:lzekbcpn45eq3d5fysgrczumqe
*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. ...##
###
Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs
[article]

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*. ...

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

1997
*
Lecture Notes in Computer Science
*

A

doi:10.1007/3-540-63165-8_228
fatcat:ztnm5wplxfbajefrmrw4zaspfq
*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] . ...##
###
Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference

1998
*
SIAM journal on computing (Print)
*

Given an undirected

doi:10.1137/s0097539796305109
fatcat:rrc446nc4bee5g4wchm46frtoa
*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. ...##
###
A Constant-factor Approximation for Weighted Bond Cover
[article]

2021
*
arXiv
*
pre-print

We study the

arXiv:2105.00857v1
fatcat:gvai3sfc2bcvrewuajt2ckqtg4
*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] . ...##
###
Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

2016
*
Dagstuhl Reports
*

This report contains abstracts

doi:10.4230/dagrep.6.5.94
dblp:journals/dagstuhl-reports/EricksonKMM16
fatcat:wasdfgivt5fqdppfxo3iqqs2ta
*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*. ...##
###
A Linear-Time Approximation Scheme for TSP in Undirected Planar Graphs with Edge-Weights

2008
*
SIAM journal on computing (Print)
*

We give an

doi:10.1137/060649562
fatcat:qkvmtagkdvgrbobjn2zi2fgsku
*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. ...##
###
Combinatorial algorithms for feedback problems in directed graphs

2003
*
Information Processing Letters
*

We present simple combinatorial

doi:10.1016/s0020-0190(02)00491-x
fatcat:6hczz3tgo5f6tolcu4ge7c5rry
*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] . ...
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