A Fast Distributed Approximation Algorithm for Minimum Spanning Trees in the SINR Model

A fundamental problem in wireless networks is the \emph{minimum spanning tree} (MST) problem: given a set $V$ of wireless nodes, compute a spanning tree $T$, so that the total cost of $T$ is minimized. In recent years, there has been a lot of interest in the physical interference model based on SINR constraints. Distributed algorithms are especially challenging in the SINR model, because of the non-locality of the model. In this paper, we develop a fast distributed approximation algorithm for MST construction in an SINR based distributed computing model. For an $n$-node network, our algorithm’s running time is $O(D\log{n}+\mu\log{n})$ and produces a spanning tree whose cost is within $O(\log n)$ times the optimal (MST cost), where $D$ denotes the diameter of the disk graph obtained by using the maximum possible transmission range, and $\mu=\log{\frac{d_{max}}{d_{min}}}$ denotes the “distance diversity” w.r.t. the largest and smallest distances between two nodes. (When $\frac{d_{max}}{d_{min}}$ is $n$-polynomial, $\mu = O(\log n)$.) Our algorithm’s running time is essentially optimal (upto a logarithmic factor), since computing {\em any} spanning tree takes $\Omega(D)$ time; thus our algorithm produces a low cost spanning tree in time only a logarithmic factor more than the time to compute a spanning tree. The distributed scheduling complexity of the spanning tree resulted from our algorithm is $O(\mu \log n)$. Our algorithmic design techniques can be useful in designing efficient distributed algorithms for related “global” problems in wireless networks in the SINR model.

💡 Research Summary

The paper tackles one of the most fundamental global problems in wireless ad‑hoc networks – constructing a minimum‑spanning‑tree (MST) – under the physical interference model defined by Signal‑to‑Interference‑plus‑Noise Ratio (SINR). Unlike graph‑based abstractions where a transmission only affects immediate neighbours, the SINR model captures the non‑local nature of wireless propagation: a transmission may interfere with any node whose reception SINR falls below a threshold. This non‑locality makes classic distributed MST protocols (e.g., Gallager‑Humblet‑Spira) inapplicable, and any algorithm must carefully schedule transmissions to satisfy SINR constraints while still achieving a globally good tree.

Model and Notation
The network consists of (n) nodes placed in the Euclidean plane. Each node transmits with power (P); the received power at distance (d) follows the path‑loss law (P/d^{\alpha}) with exponent (\alpha>2). A reception at node (v) from sender (u) succeeds if

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