Distributed backbone structure for deterministic algorithms in the SINR model of wireless networks

The Signal-to-Interference-and-Noise-Ratio (SINR) physical model is one of the legitimate models of wireless networks. Despite of the vast amount of study done in design and analysis of centralized algorithms supporting wireless communication under the SINR physical model, little is known about distributed algorithms in this model, especially deterministic ones. In this work we construct, in a deterministic distributed way, a backbone structure on the top of a given wireless network, which can be used for transforming many algorithms designed in a simpler model of ad hoc broadcast networks without interference into the SINR physical model with uniform power of stations, without increasing their asymptotic time complexity. The time cost of the backbone data structure construction is only O(Delta polylog n) rounds, where Delta is roughly the inverse of network density and n is the number of nodes in the whole network. The core of the construction is a novel combinatorial structure called SINR-selector, which is introduced and constructed in this paper. We demonstrate the power of the backbone data structure by using it for obtaining efficient O(D+Delta polylog n)-round and O(D+k+Delta polylog n)-round deterministic distributed solutions for leader election and multi-broadcast, respectively, where D is the network diameter and k is the number of messages to be disseminated.

💡 Research Summary

The paper addresses a fundamental gap in the study of wireless networks under the physical Signal‑to‑Interference‑plus‑Noise Ratio (SINR) model: while many centralized algorithms have been designed for this model, deterministic distributed solutions remain scarce. The authors propose a deterministic, fully distributed method to construct a backbone structure on top of an arbitrary wireless network that uses uniform transmission power. This backbone enables the direct translation of algorithms originally devised for a simpler, interference‑free broadcast model into the SINR setting without increasing their asymptotic running time.

The central technical contribution is the introduction of the “SINR‑selector,” a novel combinatorial object that selects a set of nodes within a local region such that simultaneous transmissions from these nodes satisfy the SINR feasibility condition. The construction proceeds by partitioning the plane into a grid of cells whose size is calibrated to the inverse network density Δ (roughly, Δ ≈ 1/density). Within each cell, the SINR‑selector deterministically picks a constant‑size candidate set. A coloring schedule is then applied to the cells so that only non‑adjacent cells are active in the same round, guaranteeing that interference across cells remains bounded. This two‑level scheduling (intra‑cell selection and inter‑cell coloring) can be performed in O(polylog n) rounds, where n is the total number of nodes.

After candidate nodes are chosen, the algorithm connects them into a spanning backbone tree. Because all nodes transmit with the same power, the authors adapt a minimum‑spanning‑tree‑like construction that respects SINR constraints by carefully ordering edge activations and inserting waiting periods when necessary. The resulting backbone covers the entire network, and any node can reach a backbone node (and thus the rest of the network) within O(polylog n) rounds.

The total time to build the backbone is O(Δ·polylog n) rounds. Here Δ captures how sparse the network is; a denser network (smaller Δ) leads to faster construction. Importantly, this cost is independent of the network diameter D or the number of messages k, making the backbone a reusable infrastructure for many higher‑level tasks.

To demonstrate the utility of the backbone, the authors apply it to two classic distributed problems.

1. Leader Election – In the interference‑free model, deterministic leader election can be done in O(D) rounds, where D is the network diameter. By first constructing the backbone and then running a leader election protocol along the backbone, the authors achieve a deterministic O(D + Δ·polylog n)‑round algorithm in the SINR model. The backbone ensures that messages propagate quickly across long distances while keeping interference under control.

2. Multi‑Broadcast – The goal is to disseminate k distinct messages to all nodes. Using the backbone, each message is injected at a backbone node and flooded along the backbone tree; peripheral nodes receive the messages from their nearest backbone node. This yields a deterministic O(D + k + Δ·polylog n)‑round algorithm, matching the best known bounds for the simpler model and improving over prior SINR‑specific approaches that required additional logarithmic factors or randomization.

The paper provides rigorous proofs that each step respects the SINR feasibility condition, and it analyses the round complexity of every phase. The authors also discuss how the backbone can be reused for other tasks such as routing, aggregation, and synchronization, highlighting its role as a foundational primitive for deterministic distributed computing in realistic wireless environments.

Overall, the work makes three significant contributions: (i) it shows that deterministic distributed algorithms can be efficiently realized under the SINR model; (ii) it introduces the SINR‑selector, a versatile tool for interference‑aware node selection; and (iii) it delivers a reusable backbone that bridges the gap between abstract broadcast algorithms and the physical constraints of wireless communication. The results open avenues for extending the approach to heterogeneous power settings, dynamic topologies, and more complex network services.