Online capacity maximization in wireless networks

Abstract

In this paper we study a dynamic version of capacity maximization is the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the channel. Accepted requests must satisfy constraints on the signal-to-interference-plus-noise (SINR) ratio. The objective is to maximize the number of accepted requests.Using competitive analysis we study algorithms using distance-based power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1, Δ] and duration in [1, Γ] we derive a lower bound of Ω(Γ ⋅ Δ d/2) on the competitive ratio of any deterministic online algorithm using a distance-based power assignment. Our main result is a near-optimal deterministic algorithm that is O(Γ ⋅ Δ (d/2)+e)-competitive, for any constant e > 0.Our algorithm for a single channel can be generalized to k channels. It can be adjusted to yield a competitive ratio of O(k ⋅ Γ 1/k' ⋅ Δ(d/2k)+e) for any factorization (k', k) such that k' ⋅ k'' = k. This illustrates the effectiveness of multiple channels when dealing wite unknown request sequences. In particular, for Θ(log Γ ⋅ log Δ) channels this yields an O(log Γ ⋅ log Δ)-competitive algorithm. Additionally, we show how this approach can be turned into a randomized algorithm, which is O(log Γ ⋅ log Δ)-competitive even for a single channel.