Discrete Mathematics - Topics on domination
Next century challenges: mobile networking for “Smart Dust”
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
Transmission scheduling in ad hoc networks with directional antennas
Proceedings of the 8th annual international conference on Mobile computing and networking
Wireless sensor networks: a survey
Computer Networks: The International Journal of Computer and Telecommunications Networking
Random channel assignment in the plane
Random Structures & Algorithms
A Random Graph Model for Optical Networks of Sensors
IEEE Transactions on Mobile Computing
The distant-2 chromatic number of random proximity and random geometric graphs
Information Processing Letters
Asymptotic connectivity in wireless ad hoc networks using directional antennas
IEEE/ACM Transactions on Networking (TON)
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Random scaled sector graphs were introduced as a generalization of random geometric graphs to model networks of sensors using optical communication. In the random scaled sector graph model vertices are placed uniformly at random into the [0, 1]2 unit square. Each vertex i is assigned uniformly at random sector Si, of central angle αi, in a circle of radius ri (with vertex i as the origin). An arc is present from vertex i to any vertex j, if j falls in Si. In this work, we study the value of the chromatic number χ(Gn), directed clique number ω(Gn), and undirected clique number ω2 (Gn) for random scaled sector graphs with n vertices, where each vertex spans a sector of α degrees with radius rn = √ln n/n. We prove that for values α n → ∞ w.h.p., χ(Gn) and ω2 (Gn) are Θ(ln n/ln ln n), while ω(Gn) is O(1), showing a clear difference with the random geometric graph model. For α π w.h.p., χ(Gn) and ω2 (Gn) are Θ (ln n), being the same for random scaled sector and random geometric graphs, while ω(Gn) is Θ(ln n/ln ln n).