Journal ArticleDOI
NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
Harry B. Hunt,Madhav V. Marathe,Venkatesh Radhakrishnan,S. S. Ravi,Daniel J. Rosenkrantz,Richard Edwin Stearns +5 more
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TLDR
The approximation schemes for hierarchically specified unit disk graphs presented in this paper are among the first approximation schemes in the literature for natural PSPACE-hard optimization problems.About:
This article is published in Journal of Algorithms.The article was published on 1998-02-01. It has received 345 citations till now. The article focuses on the topics: Indifference graph & Chordal graph.read more
Citations
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Book ChapterDOI
Minimum dominating set approximation in graphs of bounded arboricity
TL;DR: This paper compromises between generality and efficiency by considering the problem on graphs of small arboricity a, which includes, but is not limited, graphs excluding fixed minors, such as planar graphs, graphs of (locally) bounded treewidth, or bounded genus.
Journal ArticleDOI
A 5+epsilon (Porson)-approximation algorithm for minimum weighted dominating set in unit disk graph
Decheng Dai,Changyuan Yu +1 more
TL;DR: Combining the common technique used in the above mentioned reference, this work can compute a minimum weight connected dominating set with approximation ratio 9+epsilon (Porson) in the same work, beating the previous best result of 10+.
Journal ArticleDOI
Approximating Layout Problems on Random Geometric Graphs
TL;DR: This paper proves that some of the layout problems on a family of random geometric graphs remain NP-complete even for geometric graphs, and presents two heuristics that, almost surely, turn out to be constant approximation algorithms for their layout problems.
Journal ArticleDOI
Optimization problems in multiple-interval graphs
TL;DR: In this paper, the authors give a (2−1/t)-approximation algorithm for Minimum Vertex Cover, which also works when a t-interval representation of the given graph is absent.
Journal ArticleDOI
Distributed spanners with bounded degree for wireless ad hoc networks
TL;DR: It is shown that the Yao plus reverse Yao graph has a bounded power stretch factor 2 in civilized unit disk graph, and the symmetric Yao graph does not have a constant bounded stretch factor.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.