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
The Homogeneous Broadcast Problem in Narrow and Wide Strips I: Algorithms
TL;DR: This work describes several algorithms for both the regular and the hop-bounded versions of the broadcast problem, and shows that both problems are solvable in polynomial time in strips of small constant width.
Dissertation
Optimisation de la capacité et de la consommation énergétique dans les réseaux maillés sans fil
TL;DR: In this paper, the authors define the capacite d a reseau as the quantite de trafic that le reseau peut supporter par unite de temps, and propose an architecture of communication basee based on CSMA/CA and TDMA.
Dissertation
Approximation and online algorithms in scheduling and coloring
TL;DR: A general method is presented which leads to the design of polynomial time approximation schemes (PTASs) and best possible approximation results for a number of scheduling and labeling (coloring) problems.
Book ChapterDOI
Cover contact graphs
Nieves Atienza,Natalia de Castro,Carmen Cortés,M. Ángeles Garrido,Clara I. Grima,Gregorio Hernández,Alberto Márquez,Auxiliadora Moreno,Martin Nöllenburg,José R. Portillo,Pedro Reyes,Jesús Valenzuela,María Trinidad Villar,Alexander Wolff +13 more
TL;DR: It is shown that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds), and efficient algorithms are given for the case that seeds are points and covers are disks or triangles.
Journal ArticleDOI
Coloring the complements of intersection graphs of geometric figures
Seog-Jin Kim,Kittikorn Nakprasit +1 more
TL;DR: The chromatic number of the complement of the intersection graph of homothetic copies of a fixed convex body in R^n is studied.
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.