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
Shifting Coresets: Obtaining Linear-Time Approximations for Unit Disk Graphs and Other Geometric Intersection Graphs
TL;DR: A variation of the known shifting strategy that allows for linear-time constant-factor approximation algorithms for problems on unit disk graphs is introduced, bringing significant performance improvements when compared to previous algorithms that achieve the same approximation ratios.
Journal ArticleDOI
Optimal Scheduling for Dynamic Channel Allocation in Wireless LANs
TL;DR: Under broad traffic assumptions, it is proved that the attainable system throughput can be optimized by scheduling APs and allocating channels in each frame such that a weighted sum of queue sizes at the activated APs is maximized.
Proceedings ArticleDOI
Towards Sub-Quadratic Diameter Computation in Geometric Intersection Graphs
TL;DR: This work (conditionally) rule out sub-quadratic algorithms in several classes of intersection graphs, i.e., algorithms of running time O ( n 2 − δ ) for some δ > 0.05, and gives an algorithm that distinguishes between diameter 2 and 3 in near-linear time.
Book ChapterDOI
Minimum Interference Planar Geometric Topology in Wireless Sensor Networks
Trac N. Nguyen,Dung T. Huynh +1 more
TL;DR: It is shown that the problem of assigning power to nodes in the plane to yield a planar geometric graph whose nodes have bounded interference is NP-complete under both interference definitions.
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.