Unit disk graphs
Brent N. Clark,Brent N. Clark,Charles J. Colbourn,Charles J. Colbourn,David S. Johnson,David S. Johnson +5 more
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TLDR
It is shown that many standard graph theoretic problems remain NP-complete on unit disks, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs.About:
This article is published in Discrete Mathematics.The article was published on 1991-01-02 and is currently open access. It has received 1525 citations till now. The article focuses on the topics: Indifference graph & Chordal graph.read more
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Book ChapterDOI
On Enhancing Fault Tolerance of Virtual Backbone in a Wireless Sensor Network with Unidirectional Links
Ravi Tiwari,My T. Thai +1 more
TL;DR: This chapter proposes solutions for efficient construction of a fault tolerant virtual backbone in a WSN where the sensor nodes have different transmission ranges and formulation of the problem as a k-Strongly Connected m-Dominating and Absorbing Set (k, m) SCDAS problem.
Journal ArticleDOI
Maximal Independent Sets in Heterogeneous Wireless Ad Hoc Networks
TL;DR: T tighter upper bounds for the size of MISs in heterogeneous wireless ad hoc networks are given when the maximum and minimum transmission range are relatively close, and this result is much better.
Proceedings ArticleDOI
Broadcasting in logarithmic time for ad hoc network nodes on a line using mimo
TL;DR: The logarithmic time broadcast algorithm which takes advantage of the MISO power gain by self-coordinating wireless nodes and proves that in the free space model no diversity gain can be expected for MIMO.
Journal ArticleDOI
Linear embeddings of graphs and graph limits
TL;DR: In this article, the authors define a new graph parameter? *, which aims to measure the similarity of the graph to an instance of a random graph with a linear embedding, and show that the behaviour of? * is consistent with the notion of convergence as defined in the theory of dense graph limits.
Journal ArticleDOI
Approximating Common Control Channel Problem in Cognitive Radio Networks
Ram Narayan Yadav,Rajiv Misra +1 more
TL;DR: It is proved that the CCC assignment problem is NP-hard (nondeterministic polynomial-time hard) by reduction using minimum dominating set problem and the proposed scheme outperforms with the competitive schemes.
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.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Book
Algorithmic graph theory and perfect graphs
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
Journal ArticleDOI
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.