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.
We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data-access cost. We introduce the data placement problem to model this problem. We have a set of caches @math , a set of clients @math , and a set of data objects @math . Each cache @math can store at most @math data objects. Each client @math has demand @math for a specific data object @math and has to be assigned to a cache that stores that object. Storing an object @math in cache @math incurs a storage cost of @math , and assigning client @math to cache @math incurs an access cost of @math . The goal is to find a placement of the data objects to caches respecting the capacity constraints, and an assignment of clients to caches so as to minimize the total storage and client access costs. We present a 10-approximation algorithm for this problem. Our algorithm is based on rounding an optimal solution to a natural linear-programming relaxation of the problem. One of the main technical challenges encountered during rounding is to preserve the cache capacities while incurring only a constant-factor increase in the solution cost. We also introduce the connected data placement problem to capture settings where write-requests are also issued for data objects, so that one requires a mechanism to maintain consistency of data. We model this by requiring that all caches containing a given object be connected by a Steiner tree to a root for that object, which issues a multicast message upon a write to (any copy of) that object. The total cost now includes the cost of these Steiner trees. We devise a 14-approximation algorithm for this problem. We show that our algorithms can be adapted to handle two variants of the problem: (a) a @math -median variant, where there is a specified bound on the number of caches that may contain a given object, and (b) a generalization where objects have lengths and the total length of the objects stored in any cache must not exceed its capacity. We consider the problem of proactive retention aware caching in a heterogeneous wireless edge network consisting of mobile users accessing content from a server and associated to one or more edge caches. Our goal is to design a caching policy that minimizes the sum of content storage costs and server access costs over two design variables: the retention time of each cached content and the probability that a user routes content requests to each of its associated caches. We develop a model that captures multiple aspects such as cache storage costs and several capabilities of modern wireless technologies, such as server multicast unicast transmissions, device multi-path routing, and cache access constraints. We formulate the problem of Proactive Retention Routing Optimization as a non-convex, non-linear mixed-integer program. We prove that it is NP-hard under both multicast unicast modes—even when the caches have a large capacity and storage costs are linear—and develop greedy algorithms that have provable performance bounds for the case of uncapacitated caches. Finally, we propose heuristics with low computational complexity for the capacitated cache case as well as for the case of convex storage costs. Systematic evaluations based on real-world data demonstrate the effectiveness of our approach, compared to the existing caching schemes.  The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep ij and incurs a cost ofc ij ; each machinei is available forT i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T i time units. Many distributed systems rely on neighbor selection mechanisms to create overlay structures that have good network performance. These neighbor selection mechanisms often assume the triangle inequality holds for Internet delays. However, the reality is that the triangle inequality is violated by Internet delays. This phenomenon creates astrange environment that confuses neighbor selection mechanisms. This paper investigates the properties of triangle inequality violation (TIV) in Internet delays, the impacts of TIV on representative neighbor selection mechanisms, specifically Vivaldi and Meridian, and avenues to reduce these impacts. We propose a TIV alert mechanism that can inform neighbor selection mechanisms to avoid the pitfalls caused by TIVs and improve their effectiveness. Video on-demand streaming from Internet-based servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as “helpers”). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of 1-(1-1 d )d, where d is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes.