arXiv:2611.16844 · v1

Locality Meets Interference: Structure and Scheduling in Radio Multicasting

首次提交 2026-11-12 22:18

版本更新 2026-11-12 22:18

雷达观测 2026-11-13 14:15

摘要

We study multipoint-to-multipoint multicasting in synchronous radio networks with unknown participant locations and unrestricted message aggregation. Let $n$ be the network size, $k$ the number of participants, and $d$ their hop diameter. A supplied distance-two coloring with $C$ colors yields completion within $(C-1)d+1$ slots and at most $nk$ transmissions. In unit disk graphs, coordinates, one-hop neighbor data, and a common degree bound $Δ_0$ suffice for a $15(Δ_0+1)$-color schedule. A known fixed separation bound permits optimal deterministic $Θ(d)$ completion from coordinates alone. Without geometric data, strong selectivity gives $O(d\min\{n,(Δ_0+1)^2\log n\})$ slots when $n$ is known. Independent random transmission gives $O((Δ_0+1)(d+\log(k/η)))$ slots with failure probability at most $η$; for fixed $Δ_0$, this simplifies to $O(d+\log(1/η))$. A star construction shows that the logarithmic term is necessary for this random rule when the degree grows. We extend color schedules to fixed deletions and subgraphs connected over bounded windows of cycles. Separate conditional reductions preserve additive costs under diameter guessing and control parameter-table and cluster preprocessing. Finally, a counterexample shows that pruning and reranking a breadth-first tree can destroy interference-free delivery. For one-hop designated delivery with receiver degree at most $b$, we prove that the optimal schedule length equals the chromatic number of an associated conflict graph and is at most $2b-1$, with matching examples.

作者备注：21 pages