Approximation Algorithms for Bandwidth and Storage Allocation

We discuss two NP-hard allocation problems, the Bandwidth Allocation Problem (BAP) and the Storage Allocation Problem (SAP). In BAP we are given a set of requests, each of which is associated with a time interval, a bandwidth demand, and a profit. A feasible solution is a subset of requests such that at any given time the total bandwidth given to allocated requests does not exceed the available bandwidth. Our goal is to find a feasible solution of maximum total profit. SAP is a variation of BAP in which we are given two additional constraints: (i) the specific portion of the resource allocated to a request cannot change during the time interval of the request, and (ii) the allocation of the resource must be contiguous. We present two deterministic polynomial-time approximation algorithms one for BAP and the other for SAP. The performance guarantee of both algorithms is (2 + 1/(e− 1))−1 − ǫ ≈ 1/2.582. The best previously known deterministic approximation ratio for BAP is 1/3 (randomized 1/2), and the best previously known ratio for SAP is 1/7. The algorithms are based on a new application of the Local Ratio technique in which a series of approximations is packed into narrow bandwidth slices.