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
Citations
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Journal ArticleDOI
Finding minimum weight connected dominating set in stochastic graph based on learning automata
TL;DR: It is proved that by the proper choice of the learning rate, the probability of finding the MCDS is close enough to unity.
Proceedings ArticleDOI
A Constant Approximation Algorithm for Interference Aware Broadcast in Wireless Networks
TL;DR: This paper studies a more general model in which interference is distinguished from collision, and proposes a simple and yet efficient interference and collision free broadcast protocol that consistently outperforms the previous algorithms.
Journal ArticleDOI
Maximal independent set, weakly-connected dominating set, and induced spanners in wireless ad hoc networks
TL;DR: This paper presents two distributed algorithms for constructing a WCDS for wireless ad hoc networks in linear time, one of which is fully localized, and does not depend on the spanning tree, which makes the maintenance of the WCDS simpler, and guarantees thetenance of the same approximation ratio.
Book ChapterDOI
Algorithms for dominating set in disk graphs: breaking the log n Barrier
Matt Gibson,Imran A. Pirwani +1 more
TL;DR: A randomized algorithm is given that obtains a dominating set whose weight is within a factor 2O(log* n) of a minimum cost solution, with high probability - the technique follows the framework proposed recently by Varadarajan.
Journal ArticleDOI
CANS: Towards Congestion-Adaptive and Small Stretch Emergency Navigation with Wireless Sensor Networks
TL;DR: CANS is the first WSN-assisted emergency navigation algorithm achieving both mild congestion and small stretch, where all operations are in-situ carried out by cyber-physical interactions among people and sensor nodes.
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.