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
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Overlay network construction in highly decentralized networks
TL;DR: Results show that the first polynomial time logarithmic approximation algorithm is presented for this problem and an almost tight lower bound on the approximation ratio is presented.
Book ChapterDOI
Optimal gossiping in directed geometric radio networks in presence of dynamical faults
TL;DR: In this article, a deterministic fault-tolerant gossiping protocol for directed geometric radio networks (GRNs) is proposed, where every node can send at most one message per time slot.
Mobile data collectors in wireless sensor networks
TL;DR: This work designs optimization schemes for routing and placement of mobile data collectors in WSNs and shows that this approach has the potential to prolong the lifetime of the network significantly.
Learning on finite metric spaces
Martin Anthony,Joel Ratsaby +1 more
TL;DR: This paper considers how to generalize the notion of sample width so that it can apply where the classifiers map from some finite metric space, and obtains generalization error bounds that depend on the sample width and on certain measures of ‘density’ of the underlying metric space.
Case Study: Dominating Sets in Planar Graphs
TL;DR: This paper presents the first distributed algorithm approximating a minimum dominating set on a planar graph within a constant factor in constant time, and the nodes do not need any additional information.
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.