Mobile edge computing (MEC) is a promising technique for providing low-latency access to services at the network edge. The services are hosted at various types of edge nodes with both computation and communication capabilities. Due to the heterogeneity of edge node characteristics and user locations, the performance of MEC varies depending on where the service is hosted. In this paper, we consider such a heterogeneous MEC system, and focus on the problem of placing multiple services in the system to maximize the total reward. We show that the problem is NP-hard via reduction from the set cover problem, and propose a deterministic approximation algorithm to solve the problem, which has an approximation ratio that is not worse than @math . The proposed algorithm is based on two sub-routines that are suitable for small and arbitrarily sized services, respectively. The algorithm is designed using a novel way of partitioning each edge node into multiple slots, where each slot contains one service. The approximation guarantee is obtained via a specialization of the method of conditional expectations, which uses a randomized procedure as an intermediate step. In addition to theoretical guarantees, simulation results also show that the proposed algorithm outperforms other state-of-the-art approaches.
Our problem is a special case of the @math -column sparse packing problem studied in @cite_6 , where a randomized approximation algorithm is proposed. Applying the approach in @cite_6 to our case, one can get an algorithm with an approximation ratio of @math (see [Appendix ] techReportThisPaper for details). (see Appendix for details). We improve on this result in two ways. First, we have a deterministic algorithm, which is more preferred due to its predictable behavior. Second, we have an approximation ratio that is at least @math , which is better.
@cite_6
782508147
We give new approximation algorithms for packing integer programs (PIPs) by employing the method of randomized rounding combined with alterations. Our first result is a simpler approximation algorithm for general PIPs which matches the best known bounds, and which admits an efficient parallel implementation. We also extend these results to a multi-criteria version of PIPs. Our second result is for the class of packing integer programs (PIPs) that are column sparse, i. e., where there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+ o(k))-approximation algorithm for k-column sparse PIPs, improving over previously known O(k 2 )-approximation ratios. We also generalize our result to the case of maximizing non-negative monotone submodular functions over k-column sparse packing constraints, and obtain an e 2k