Online capacity maximization in wireless networks

In this paper we study a dynamic version of capacity maximization in 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 request. 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)+ε )-competitive, for any constant ε>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″)+ε ) for any factorization (k′,k″) such that k′?k″=k. This illustrates the effectiveness of multiple channels when dealing with 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.