Paper Info
Title
Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class.
Abstract
We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world networks) while still guaranteeing approximation ratios. The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution to apply to the original graph. We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as INDEPENDENT SET, VERTEX COVER, FEEDBACK VERTEX SET, MINIMUM MAXIMAL MATCHING, CHROMATIC NUMBER, (l-)DOMINATING SET, EDGE (l-)DOMINATING SET, and CONNECTED DOMINATING SET. To enable this framework, we develop new editing algorithms that find the approximately-fewest edits required to bring a given graph into one of a few important graph classes (in some cases these are bicriteria algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family). For bounded degeneracy, we obtain an O(r log n)-approximation and a bicriteria (4, 4)-approximation which also extends to a smoother bicriteria trade-off. For bounded treewidth, we obtain a bicriteria (O(log(1.5) n), O(root logw))-approximation, and for bounded pathwidth, we obtain a bicriteria (O(log(1.5) n), O(root log w center dot log n))-approximation. For treedepth 2 (related to bounded expansion), we obtain a 4-approximation. We also prove complementary hardness-of-approximation results assuming P not equal NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant factor 2 (assuming UGC).
Year
DOI
Venue
2018
10.4230/LIPIcs.ESA.2019.37
Leibniz International Proceedings in Informatics
Keywords
Field
DocType
structural rounding,graph editing,approximation algorithms
Approximation algorithm,Discrete mathematics,Dominating set,Combinatorics,Matching (graph theory),Independent set,Vertex cover,Treewidth,Pathwidth,Mathematics,Feedback vertex set
Journal
Volume
ISSN
Citations 
144
1868-8969
0
PageRank 
References 
Authors
0.34
0
8
Name
Order
Citations
PageRank
erik d demaine121616.91
Timothy D. Goodrich252.15
Kyle Kloster3795.72
Brian Lavallee400.34
Quanquan Liu577.90
Blair D. Sullivan610213.93
Ali Vakilian7124.60
Andrew van der Poel810.72