# Service Placement with Provable Guarantees in Heterogeneous Edge Computing Systems

## TL;DR

This paper addresses the complex problem of optimally placing multiple services in heterogeneous mobile edge computing systems, providing a provably near-optimal deterministic algorithm with strong theoretical and empirical performance guarantees.

## Contribution

It introduces a novel approximation algorithm with a proven ratio for service placement in heterogeneous MEC, including a unique node partitioning method and theoretical analysis.

## Key findings

- The problem is NP-hard, confirmed by reduction from set cover.
- The proposed algorithm achieves an approximation ratio of at least (1 - e^{-1})/4.
- Simulation results show the algorithm outperforms existing methods.

## Abstract

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 $\left(1-e^{-1}\right)/4$. 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.