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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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
A scalable key management and clustering scheme for wireless ad hoc and sensor networks
TL;DR: The distributed, efficient clustering approach (DECA) provides robust clustering to form subgroups, and analytical and simulation results demonstrate that DECA is energy-efficient and resilient against node mobility.
Book ChapterDOI
Discrete Mathematics and Radio Channel Assignment
TL;DR: The following generalization of graph colouring arises naturally in the study of channel assignment for cellular radiocommunications networks.
Journal ArticleDOI
Threshold Functions for Random Graphs on a Line Segment
TL;DR: In this article, the authors consider the asymptotics of the model of random graphs suggested by Gilbert and show that every upward closed property of ordered graphs has at least a weak threshold in this model on this metric space.
Proceedings ArticleDOI
An incremental algorithm for broadcast scheduling in packet radio networks
Xiaopeng Ma,Errol L. Lloyd +1 more
TL;DR: The feasibility of simultaneously meeting the twin objectives of much faster execution (than an off-line algorithm) and the production of a high quality schedule is established, by presenting an incremental algorithm for broadcast scheduling.
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On the Power of Uniform Power: Capacity of Wireless Networks with Bounded Resources
TL;DR: This paper proves that in one-dimensional settings the capacity of a non-uniform assignment exceeds a uniform assignment by at most a factor of O(logL max ) when the length of the network is L max, and determines the maximum factor by which a non -uniform power assignment can outperform the uniform case in the SINR model.
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.