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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Journal ArticleDOI
Geometric separation and exact solutions for the parameterized independent set problem on disk graphs
Jochen Alber,Jiří Fiala +1 more
TL;DR: In this paper, the authors considered the problem of partitioning disk graphs of bounded radius ratio and showed that the problem is fixed parameter tractable with running time 2O(√k) + nO(1) for a given set of n disks in the Euclidean plane, where k is a set of k non-intersecting disks.
Proceedings ArticleDOI
Local approximation schemes for ad hoc and sensor networks
TL;DR: Two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs are presented andgraphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models.
Journal ArticleDOI
A better constant-factor approximation for weighted dominating set in unit disk graph
TL;DR: This paper presents a (10+ε)-approximation algorithm to compute minimum-weight connected dominating set (MWCDS) in unit disk graph, which computes a dominating set which has approximation ratio 6+ε (ε is an arbitrary positive number).
Journal ArticleDOI
Independent set of intersection graphs of convex objects in 2D
TL;DR: In this article, the problem of computing a maximum independent set in the intersection graph of a set of objects is known to be NP-complete for most cases in two and higher dimensions.
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.