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Greedy Forwarding algorithm is a widely-used routing algorithm for wirelessnetworks. However, it can fail if network topologies (usually modeled bygeometric graphs) contain voids. Since Yao Graph and Theta Graph are two typesof geometric graphs exploited to construct wireless network topologies, thispaper studies whether these two types of graphs can contain voids.Specifically, this paper shows that when the number of cones in a Yao Graph orTheta Graph is less than 6, Yao Graph and Theta Graph can have voids, but whenthe number of cones equals or exceeds 6, Yao Graph and Theta Graph are free ofvoids.

Are Yao Graph and Theta Graph Void Free?