Near-Shortest Path Routing in Hybrid Communication Networks

TL;DR

This paper develops a deterministic routing scheme for hybrid networks modeled as unit-disc graphs, achieving constant stretch with small labels and routing tables in logarithmic rounds, advancing fundamental network routing theory.

Contribution

It introduces a novel deterministic routing scheme for near-shortest paths in hybrid networks modeled as unit-disc graphs, with optimal size and speed.

Findings

Routing scheme has constant stretch.

Labels and tables are of size O(log n).

Routing computed in O(log n) rounds.

Abstract

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 $\mathsf{HYBRID}$ 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 $\mathsf{HYBRID}$ 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.