Compact Routing in Unit Disk Graphs

Mulzer, Wolfgang; Willert, Max

doi:10.4230/lipics.isaac.2020.16

Cited by 2 publications

(1 citation statement)

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“…Using the well-separated pair decomposition (WSPD) for UDGs [14], Kaplan et al [19] present a local routing scheme with stretch 1+ε with node labels, routing tables and headers of size polynomial in log n, log D, and 1/ε, where D is the diameter of UDG(V ). Later, [26] shows how to achieve a stretch of 1+ε without using dynamic headers.…”

Section: Related Workmentioning

confidence: 99%

Near-Shortest Path Routing in Hybrid Communication Networks

Coy¹,

Czumaj²,

Feldmann³

et al. 2022

Preprint

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Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA'20] introduced the HYBRID model, which is based on the concept of synchronous message passing and uses two fundamentally different principles of communication: a local mode, which allows every node to exchange one message per round with each neighbor in a local communication graph; and a global mode where any pair of nodes can exchange messages, but only few such exchanges can take place per round. A sizable portion of the previous research for the HYBRID model revolves around basic communication primitives and computing distances or shortest paths in networks. In this paper, we extend this study to a related fundamental problem of computing compact routing schemes for near-shortest paths in the local communication graph. We demonstrate that, for the case where the local communication graph is a unit-disc graph with n nodes that is realized in the plane and has no radio holes, we can deterministically compute a routing scheme that has constant stretch and uses labels and local routing tables of size O(log n) bits in only O(log n) rounds.

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Section: Related Workmentioning

confidence: 99%