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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Statistically assisted routing algorithms (SARA) for hop count based forwarding in wireless sensor networks
TL;DR: The results show that the exploitation of second order cost information in SARA substantially increases the goodness of the selected paths with respect to fully localized greedy routing.
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Approximation Algorithms for Intersection Graphs
Frank Kammer,Torsten Tholey +1 more
TL;DR: The similarity to chordal graphs is used to construct simple polynomial-time approximation algorithms with constant approximation ratio for many NP-hard problems, when restricted to graphs for which at least one of the three complexity parameters is bounded by a constant.
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On construction of quality fault-tolerant virtual backbone in wireless networks
TL;DR: This paper proposes a new strategy for computing a smaller-size 3-connected m-dominating set in a unit disk graph with any m ≥ 1 and shows the approximation ratio of the algorithm is constant and its running time is polynomial.
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MiFi: a framework for fairness and QoS assurance for current IEEE 802.11 networks with multiple access points
Yigal Bejerano,Randeep Bhatia +1 more
TL;DR: This paper presents a framework for providing fair service and supporting quality of service (QoS) requirements in IEEE 802.11 networks with multiple access points (APs) and shows that such a system can be implemented without requiring any modification of the underlying MAC protocol standard or the behavior of the mobile stations.
Fast Distributed Well Connected Dominating Sets for Ad Hoc Networks
TL;DR: This work presents a fast distributed implementation of D2-coloring for ad hoc networks which is guaranteed to use at most O(1) times the number of colors required by the optimal algorithm, and combines the properties of WCDS with other ideas to obtain the following interesting applications.
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.
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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.