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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Proceedings ArticleDOI
Research on a location-based task assignment for mobile sensing
Xiulan Wang,Shiyan Wang +1 more
TL;DR: It turns out that the practical performance of the proposed near optimal task assignment algorithm corroborates the theoretical analysis.
Proceedings ArticleDOI
An n O(1/ϵ) Approximation Scheme For The Minimum Dominating Set In Unit Disk Graphs
TL;DR: The key ingredient is an improved dynamic programming algorithm that depends exponentially on a more essential 1-dimensional “width” of the problem that gives an asymptotic improvement over the best known PTAS.
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A Linear-Time Algorithm for Minimum k-Hop Dominating Set of a Cactus Graph.
TL;DR: To achieve this, it is shown that the k-dominating set problem on unicycle graph reduces to the piercing circular arcs problem, and a linear-time algorithm for piercing sorted circular arcs is shown, which improves the best known $O(n\log n)$- time algorithm.
Proceedings ArticleDOI
Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs
TL;DR: In this paper , a relaxation of the notion of treewidth-fragility, namely tree-independence-numberfragile, was investigated, and polynomial-time approximation schemes for independent packing problems on fractionally tree independence-number-fraggile graph classes were obtained.
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Approximation and parameterized algorithms for geometric independent set with shrinking
TL;DR: This work improves and significantly simplifies a PTAS given earlier for this problem, and provides the first parameterized results for the shrinking model, and explores kernelization in theshrunk model, by giving efficient kernelization procedures for several variants of the problem when the input rectangles are squares.
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.