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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Journal ArticleDOI
Towards broadcast redundancy minimization in duty‐cycled wireless sensor networks
TL;DR: The proposed scheme, Broadcast Redundancy Minimization Scheduling (BRMS), finds a set of forwarding nodes, which minimizes the number of broadcast transmissions, and constructs a forest of sub-trees based on the relationship between each forwarding node and its corresponding receivers.
Journal ArticleDOI
First responder communication in urban environments
TL;DR: The implications of an emergency switch for privately owned wireless routers, which can transition to an emergency mode to create a supportive wireless mesh network, are discussed and real data from wireless routers in a city is gathered.
Book ChapterDOI
Heuristic algorithms for constructing connected dominating sets with minimum size and bounded diameter in wireless networks
TL;DR: The diameter is considered as a quality factor for CDS construction, and two new heuristic algorithms are developed that have constant ratios 9 and 3 for its size and diameter, respectively.
Proceedings ArticleDOI
Testing bipartiteness of geometric intersection graphs
TL;DR: This work shows how to test the bipartiteness of an intersection graph of n line segments or simple polygons in the plane, or of balls in Rd, in time O(n log n), and finds subquadratic algorithms for connectivity and bipartitism testing of intersection graphs of a broad class of geometric objects.
Journal IssueDOI
Efficient clusterhead rotation via domatic partition in self-organizing sensor networks
Rajiv Misra,Chittaranjan Mandal +1 more
TL;DR: This work developed a distributed self-organizing one-domatic partitioning scheme with approximation factor of at least 1-16 for unit-disk-graphs (UDGs) and demonstrated through simulations that the benefits ofSelf-organization is achieved without sacrificing the quality of domatic partitioned.
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.