Edge computing, which is a fundamental component of emerging 5G architectures, involves onloading or offloading multiple virtual network functions from mobile devices to an edge network substrate. In this paper, we present a model for the complete edge function onloading problem, which consists of three main phases: (1) Cyber foraging, which involves discovery of resources monitoring the state of edge resources, (2) edge function mapping, which involves matching requests to available resources, and (3) allocation, which involves assigning resources to mappings. Using optimization theory, we show how these three phases are tightly connected, and how the wide spectrum of existing solutions that either solve a particular phase, or jointly solve two of the phases (along with their interactions), are incomplete and may lead to inefficiencies. Moreover, with extensive simulation experiments we demonstrate that joint optimization of all three phases enables the edge network to host a larger set of constrained edge function requests.

We propose an embedding and routing scheme for arbitrary network connectivity graphs, based on greedy routing and utilizing virtual node coordinates. In dynamic multihop packet-switching communication networks, routing elements can join or leave during network operation or exhibit intermittent failures. We present an algorithm for online greedy graph embedding in the hyperbolic plane that enables incremental embedding of network nodes as they join the network, without disturbing the global embedding. Even a single link or node removal may invalidate the greedy routing success guarantees in network embeddings based on an embedded spanning tree subgraph. As an alternative to frequent reembedding of temporally dynamic network graphs in order to retain the greedy embedding property, we propose a simple but robust generalization of greedy distance routing called Gravity-Pressure (GP) routing. Our routing method always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding. GP routing does not require precomputation or maintenance of special spanning subgraphs and, as demonstrated by our numerical evaluation, is particularly suitable for operation in tandem with our proposed algorithm for online graph embedding.

This paper describes a randomized algorithm for approximate counting that preserves the same modest memory requirements of log(log n) bits per counter as the approximate counting algorithm introduced in the seminal paper of R. Morris (1978), and in addition, is characterized by (i) lower expected number of memory accesses and (ii) lower standard error on more than 99 percent of its counting range. An exact analysis of the relevant statistical properties of the algorithm is carried out. Performance evaluation via simulations is also provided to validate the presented theory.