Bandwidth allocation in cellular networks with multiple interferences

We study the problem of bandwidth allocation with multiple interferences  . In this problem the input consists of a set of users and a set of base stations. Each user has a list of requests, each consisting of a base station, a frequency demand, and a profit that may be gained by scheduling this request. The goal is to find a maximum profit set of user requests SS that satisfies the following conditions: (i) SS contains at most one request per user, (ii) the frequency sets allotted to requests in SS that correspond to the same base station are pairwise non-intersecting, and (iii) the QoS received by any user at any frequency is reasonable according to an interference model. In this paper we consider two variants of bandwidth allocation with multiple interferences. In the first each request specifies a demand that can be satisfied by any subset of frequencies that is large enough. In the second each request specifies a specific frequency interval. Furthermore, we consider two interference models, multiplicative and additive. We show that these problems are extremely hard to approximate if the interferences depend on both the interfered and the interfering base stations. On the other hand, we provide constant factor approximation algorithms for both variants of bandwidth allocation with multiple interferences for the case where the interferences depend only on the interfering base stations. We also consider a restrictive special case that is closely related to the Knapsack  problem. We show that this special case is NP-hard and that it admits an FPTAS.