Sub-Modularity of Waterfilling with Applications to Online Basestation Allocation

TL;DR

This paper proves that the water-filling algorithm is sub-modular and leverages this property to develop online basestation allocation algorithms that maximize sum-rate with competitive guarantees.

Contribution

It introduces the sub-modularity of water-filling and applies it to design online algorithms for basestation assignment with provable performance bounds.

Findings

Water-filling is proven to be sub-modular.

Online algorithms achieve a competitive ratio of at most 2.

Algorithms effectively allocate users without future knowledge.

Abstract

We show that the popular water-filling algorithm for maximizing the mutual information in parallel Gaussian channels is sub-modular. The sub-modularity of water-filling algorithm is then used to derive online basestation allocation algorithms, where mobile users are assigned to one of many possible basestations immediately and irrevocably upon arrival without knowing the future user information. The goal of the allocation is to maximize the sum-rate of the system under power allocation at each basestation. We present online algorithms with competitive ratio of at most 2 when compared to offline algorithms that have knowledge of all future user arrivals.