TY - JOUR

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:
A preliminary version of this work has been published at the 21st International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2018). Akanksha Agrawal is currently funded by the PBC Fellowship Program for Outstanding Post-Doctoral Researchers from China and India. Daniel Lokshtanov is currently funded by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 715744) and the United States-Israel Binational Science Foundation (Grant No. 2018302). Saket Saurabh is currently funded by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 819416) and the Swarnajayanti Fellowship (Grant No. DST/SJF/MSA01/2017-18). Meirav Zehavi is currently funded by Israel Science Foundation Grant No. 1176/18, and the United States-Israel Binational Science Foundation (Grant No. 2018302). This research has received funding from the European Research Council under ERC (Grants No. 306992 and No. 715744). Authors’ addresses: A. Agrawal (corresponding author) and M. Zehavi, Alon Building, Department of Computer Science, Ben-Gurion University of the Negev, Beersheba, Israel, 84105; emails: [email protected], [email protected]; D. Lokshtanov, 2104 Harold Frank Hall, Department of Computer Science, University of California Santa Barbara, California, 93106-5110; email: [email protected]; P. Misra, Department of Algorithms and Complexity, Max Planck Institute for Informatics, Campus E1 4, Saarland Informatics Campus, Saarbrücken, Germany, 66123; email: [email protected]; S. Saurabh, Department of Informatics, University of Bergen, Bergen, Norway, 5020, and Institute of Mathematical Sciences, HBNI, Tharamani, Chennai, India, 600113; email: [email protected]. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2020 Association for Computing Machinery. 1549-6325/2020/07-ART51 $15.00 https://doi.org/10.1145/3389338
Publisher Copyright:
© 2020 ACM.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - For a family of graphs F, the Weighted F Vertex Deletion problem, is defined as follows: given an n-vertex undirected graph G and a weight function w: V(G)→ℝ F, find a minimum weight subset S¢V(G) such that G-S belongs to F. We devise a recursive scheme to obtain O(logO(1) n)-approximation algorithms for such problems, building upon the classical technique of finding balanced separators. We obtain the first O(logO(1) n)-approximation algorithms for the following problems. •Let F be a finite set of graphs containing a planar graph, and F=G(F) be the maximal family of graphs such that every graph HϵG(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 (WP F-MFD) problem. We give a randomized and a deterministic approximation algorithms for WP F-MFD with ratios O(log1.5 n) and O(log2 n), respectively. Prior to our work, a randomized constant factor approximation algorithm for the unweighted version was known [FOCS 2012]. After our work, a deterministic constant factor approximation algorithm for the unweighted version was also obtained [SODA 2019]. •We give an O(log2 n)-factor approximation algorithm for Weighted Chordal Vertex Deletion, 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 WeightedDistance Hereditary Vertex Deletion. We believe that our recursive scheme can be applied to obtain O(logO(1) n)-approximation algorithms for many other problems as well.

AB - For a family of graphs F, the Weighted F Vertex Deletion problem, is defined as follows: given an n-vertex undirected graph G and a weight function w: V(G)→ℝ F, find a minimum weight subset S¢V(G) such that G-S belongs to F. We devise a recursive scheme to obtain O(logO(1) n)-approximation algorithms for such problems, building upon the classical technique of finding balanced separators. We obtain the first O(logO(1) n)-approximation algorithms for the following problems. •Let F be a finite set of graphs containing a planar graph, and F=G(F) be the maximal family of graphs such that every graph HϵG(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 (WP F-MFD) problem. We give a randomized and a deterministic approximation algorithms for WP F-MFD with ratios O(log1.5 n) and O(log2 n), respectively. Prior to our work, a randomized constant factor approximation algorithm for the unweighted version was known [FOCS 2012]. After our work, a deterministic constant factor approximation algorithm for the unweighted version was also obtained [SODA 2019]. •We give an O(log2 n)-factor approximation algorithm for Weighted Chordal Vertex Deletion, 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 WeightedDistance Hereditary Vertex Deletion. 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 algorithm

KW - F-Vertex Deletion

KW - Planar F-minor-free graphs

KW - balanced separators

KW - chordal graphs

KW - distance hereditary graphs

UR - http://www.scopus.com/inward/record.url?scp=85092564934&partnerID=8YFLogxK

U2 - 10.1145/3389338

DO - 10.1145/3389338

M3 - Article

AN - SCOPUS:85092564934

SN - 1549-6325

VL - 16

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 4

M1 - 3389338

ER -