[Paper Review] Arbitrary Transmission Power in the SINR Model: Local Broadcasting, Coloring and MIS

Fabian B. Fuchs, Dorothea Wagner|arXiv (Cornell University)|Feb 20, 2014

Mobile Ad Hoc Networks25 references3 citations

TL;DR

This paper introduces a novel interference bound for wireless networks with arbitrary transmission powers in the SINR model, enabling the generalization of local broadcasting, distributed coloring, and MIS algorithms to non-uniform power settings. The key contribution is a probabilistic interference bound that ensures feasibility under arbitrary power assignments, allowing algorithms to achieve near-uniform power performance bounds: $ϳ(Γ^2\Delta\log n)$ time slots for local broadcasting and $ϳ((\Delta+\ell)\Gamma^6\Delta\log n)$ for coloring, where $\Gamma$ is the max-to-min transmission range ratio and $\ell$ is the longest unidirectional chain length.

ABSTRACT

In the light of energy conservation and the expansion of existing networks, wireless networks face the challenge of nodes with heterogeneous transmission power. However, for more realistic models of wireless communication only few algorithmic results are known. In this paper we consider nodes with arbitrary, possibly variable, transmission power in the so-called physical or SINR model. Our first result is a bound on the probabilistic interference from all simultaneously transmitting nodes on receivers. This result implies that current local broadcasting algorithms can be generalized to the case of non-uniform transmission power with minor changes. The algorithms run in $Ø(Γ^{2} Δ\log n)$ time slots if the maximal degree $Δ$ is known, and $Ø((Δ+ \log n)Γ^{2} \log n)$ otherwise, where $Γ$ is the ratio between the maximal and the minimal transmission range. The broad applicability of our result on bounding the interference is further highlighted, by generalizing a distributed coloring algorithm to this setting.

Motivation & Objective

• Address the lack of algorithmic support for arbitrary transmission power in the SINR model, a critical gap for energy-efficient and scalable wireless networks.
• Enable local broadcasting in networks with heterogeneous transmission ranges and unidirectional links, which are common in real-world deployments.
• Design distributed coloring and MIS algorithms resilient to asynchronous node wake-up and unidirectional communication links under arbitrary power assignment.
• Generalize existing uniform-power algorithms to arbitrary power settings while preserving near-optimal time complexity.
• Provide a generic interference bound applicable to multiple algorithmic problems in non-uniform power wireless networks.

Proposed method

• Introduce a probabilistic interference bound based on the sum of local transmission probabilities, proving that interference remains bounded under arbitrary power assignments.
• Adapt existing local broadcasting algorithms from the uniform-power SINR model to arbitrary power by leveraging the new interference bound.
• Design a distributed node coloring algorithm that handles unidirectional links by introducing a new parameter $\ell$, measuring the longest unidirectional chain in the network.
• Modify the core coloring algorithm to allow nodes to dynamically respond to color conflicts via request-response mechanisms, ensuring color consistency.
• Simplify the coloring algorithm to compute a Maximal Independent Set (MIS) using only two colors, eliminating request states and reducing complexity.
• Ensure robustness to asynchronous node wake-up by reserving time slots for request handling and allowing nodes to re-enter the main loop upon conflict detection.

Experimental results

Research questions

• RQ1 Can local broadcasting be efficiently achieved in the SINR model when nodes use arbitrary, possibly variable, transmission powers?
• RQ2 How can interference be bounded in networks with heterogeneous transmission ranges and unidirectional links under arbitrary power assignment?
• RQ3 Can distributed coloring and MIS algorithms be designed to function correctly in directed, partially connected networks arising from arbitrary transmission powers?
• RQ4 What is the impact of asynchronous node wake-up on the correctness and runtime of coloring and broadcasting algorithms in such networks?
• RQ5 Can the performance bounds of uniform-power algorithms be preserved in the arbitrary power setting using a generic interference analysis?

Key findings

• A new interference bound is established that depends only on the sum of local transmission probabilities, enabling feasibility guarantees in arbitrary power networks.
• Local broadcasting is achieved in $\mathcal{O}(\Gamma^2\Delta\log n)$ time slots when $\Delta$ is known, and $\mathcal{O}((\Delta + \log n)\Gamma^2\log n)$ otherwise, matching uniform-power bounds.
• The distributed coloring algorithm uses $\mathcal{O}(\Gamma^2\Delta)$ colors and runs in $\mathcal{O}((\Delta + \ell)\Gamma^6\Delta\log n)$ time slots, where $\ell$ is the longest unidirectional chain.
• An MIS algorithm is derived by simplifying the coloring approach, running in $\mathcal{O}(\ell\Gamma^4\log n)$ time slots with only two colors.
• The algorithms are robust to asynchronous node wake-up and unidirectional links, with mechanisms to handle late-arriving nodes and color conflicts.
• The framework allows variable transmission power per time slot, maintaining similar performance bounds while enabling dynamic power adaptation.