TY - GEN
T1 - Polylogarithmic Approximation Algorithms for Weighted-F-Deletion Problems
AU - Agrawal, Akanksha
AU - Lokshtanov, Daniel
AU - Misra, Pranabendu
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Funding Information:
Funding This research has received funding from the European Research Council under ERC grant no. 306992 PARAPPROX, ERC grant no. 715744 PaPaALG, and ERC grant no. 725978 SYSTEMATICGRAPH.
Publisher Copyright:
© 2018 Aditya Bhaskara and Srivatsan Kumar.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - Let F be a family of graphs. A canonical vertex deletion problem corresponding to F is defined as follows: Given an n-vertex undirected graph G and a weight function w : V (G)→R+, find a minimum weight subset S V (G) such that G-S belongs to F. This is known as Weighted F Vertex Deletion problem. In this paper we devise a recursive scheme to obtain O(logO(1) n)-A pproximation algorithms for such problems, building upon the classical technique of finding balanced separators in a graph. Roughly speaking, our scheme applies to those problems, where an optimum solution S together with a well-structured set X, form a balanced separator of the input graph. In this paper, we obtain the first O(logO(1) n)-approximation algorithms for the following vertex deletion problems. Let F be a finite set of graphs containing a planar graph, and F = G(F) be the family of graphs such that every graph H2 G(F) excludes all graphs in F as minors. The vertex deletion problem corresponding to F = G(F) is the Weighted Planar F-Minor-Free Deletion (WPF-MFD) problem. We give randomized and deterministic approximation algorithms for WPF-MFD with ratios O(log1.5 n) and O(log2 n), respectively. Previously, only a randomized constant factor approximation algorithm for the unweighted version of the problem was known [FOCS 2012]. We give an O(log2 n)-factor approximation algorithm for Weighted Chordal Vertex Deletion (WCVD), the vertex deletion problem to the family of chordal graphs. On the way to this algorithm, we also obtain a constant factor approximation algorithm for Multicut on chordal graphs. We give an O(log3 n)-factor approximation algorithm for Weighted Distance Hereditary Vertex Deletion (WDHVD), also known as Weighted Rankwidth-1 Vertex Deletion (WR-1VD). This is the vertex deletion problem to the family of distance hereditary graphs, or equivalently, the family of graphs of rankwidth one. We believe that our recursive scheme can be applied to obtain O(logO(1) n)-approximation algorithms for many other problems as well.
AB - Let F be a family of graphs. A canonical vertex deletion problem corresponding to F is defined as follows: Given an n-vertex undirected graph G and a weight function w : V (G)→R+, find a minimum weight subset S V (G) such that G-S belongs to F. This is known as Weighted F Vertex Deletion problem. In this paper we devise a recursive scheme to obtain O(logO(1) n)-A pproximation algorithms for such problems, building upon the classical technique of finding balanced separators in a graph. Roughly speaking, our scheme applies to those problems, where an optimum solution S together with a well-structured set X, form a balanced separator of the input graph. In this paper, we obtain the first O(logO(1) n)-approximation algorithms for the following vertex deletion problems. Let F be a finite set of graphs containing a planar graph, and F = G(F) be the family of graphs such that every graph H2 G(F) excludes all graphs in F as minors. The vertex deletion problem corresponding to F = G(F) is the Weighted Planar F-Minor-Free Deletion (WPF-MFD) problem. We give randomized and deterministic approximation algorithms for WPF-MFD with ratios O(log1.5 n) and O(log2 n), respectively. Previously, only a randomized constant factor approximation algorithm for the unweighted version of the problem was known [FOCS 2012]. We give an O(log2 n)-factor approximation algorithm for Weighted Chordal Vertex Deletion (WCVD), the vertex deletion problem to the family of chordal graphs. On the way to this algorithm, we also obtain a constant factor approximation algorithm for Multicut on chordal graphs. We give an O(log3 n)-factor approximation algorithm for Weighted Distance Hereditary Vertex Deletion (WDHVD), also known as Weighted Rankwidth-1 Vertex Deletion (WR-1VD). This is the vertex deletion problem to the family of distance hereditary graphs, or equivalently, the family of graphs of rankwidth one. We believe that our recursive scheme can be applied to obtain O(logO(1) n)-approximation algorithms for many other problems as well.
KW - Approximation Algorithms
KW - Planar-F-Deletion
KW - Separator
UR - http://www.scopus.com/inward/record.url?scp=85052443337&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX-RANDOM.2018.1
DO - 10.4230/LIPIcs.APPROX-RANDOM.2018.1
M3 - Conference contribution
AN - SCOPUS:85052443337
SN - 9783959770859
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018
A2 - Blais, Eric
A2 - Rolim, Jose D. P.
A2 - Steurer, David
A2 - Jansen, Klaus
PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
T2 - 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018
Y2 - 20 August 2018 through 22 August 2018
ER -