TL;DR
This paper investigates the presence of voids in Yao and Theta graphs used in wireless network topologies, finding that these graphs are void-free when the number of cones is at least six.
Contribution
It establishes the critical cone count (six) at which Yao and Theta graphs become void-free, providing insights for network topology design.
Findings
Yao and Theta graphs can have voids with fewer than 6 cones.
Both graphs are void-free when the number of cones is 6 or more.
The results guide the construction of reliable wireless network topologies.
Abstract
Greedy Forwarding algorithm is a widely-used routing algorithm for wireless networks. However, it can fail if network topologies (usually modeled by geometric graphs) contain voids. Since Yao Graph and Theta Graph are two types of geometric graphs exploited to construct wireless network topologies, this paper studies whether these two types of graphs can contain voids. Specifically, this paper shows that when the number of cones in a Yao Graph or Theta Graph is less than 6, Yao Graph and Theta Graph can have voids, but when the number of cones equals or exceeds 6, Yao Graph and Theta Graph are free of voids.
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Taxonomy
TopicsMobile Ad Hoc Networks · Opportunistic and Delay-Tolerant Networks · Cooperative Communication and Network Coding