Routing Schemes for Hybrid Communication Networks in Unit-Disk Graphs
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Hybrid communication networks provide multiple modes of communication with varying characteristics. The π§πΈπ±π‘π¨π£ model was introduced to unlock theoretical study of such networks. It combines two fundamentally different communication modes. A local mode, which restricts communication among nodes to a given graph and a global mode where any two nodes may communicate in principle, but only very little such communication can take place per unit of time. We are interested in the fast computation of routing schemes, where nodes have to compute small labels and routing tables that allow for efficient routing of messages in the local network, which typically offers the majority of the throughput. Recent work has shown that using the π§πΈπ±π‘π¨π£ model admits a tremendous speed-up compared to what would be possible if either communication mode were used in isolation. However, it was also shown that the computation of routing schemes takes polynomial rounds in the π§πΈπ±π‘π¨π£ model if general graphs are used as local graph even when large labels are allowed. Coy et al. [OPODIS'21] bypass this lower bound by restricting the local graph to unit-disc-graphs, and solve the problem deterministically with running time, label size, and size of routing tables all in O(log n). However they assume that the unit disk graph has no βradio holesβ, which makes the graph much simpler (topologically similar to a tree). In this work we show how to generalize the algorithm to any unit disk graph with running time O(h^2 +log n) where h is the number of radio holes, which preserves the prior guarantees if h is small.
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