This paper studies one typical mobile edge computing (MEC) system, where a single user has some intensively calculating tasks to be computed by M nodes (ENs) with much more powerful capability. In particular, unmanned aerial vehicle (UAV) can act as the ENs due its flexibility and high mobility in deployment. For this we propose several EN selection criteria improve system whole performance of ...

Edge-independent random graphs are a model of random graphs in which each potential edge appears independently with an individual probability. Based on the relative entropy method, we determine the upper and lower bounds for the extremal vertex degrees using the edge probability matrix and its largest eigenvalue. Moreover, an application to random graphs with given expected degree sequences is ...

We prove that if T is a tree on n vertices with maximum degree ∆ and the edge probability p(n) satisfies: np ≥ C max{∆ log n, n } for some constant > 0, then with high probability the random graph G(n, p) contains a copy of T . The obtained bound on the edge probability is shown to be essentially tight for ∆ = n.

The paper concerns a certain modification of the generalized Hoede-Bakker index a notion defined for a social network of players. In the original Hoede-Bakker set up, preferences of players are involved. It is assumed that a player has an inclination either to accept or to reject a proposal, but due to the influence of others, his final decision may be different from his original inclination. I...

Geoffrey R. Grimmett Abstract. The square lattice is used to generate an oriented graph in which a rightward or upward arrow is present on each edge with probability a, and a leftward or downward arrow with probability b. Independence between different edges of the square lattice is assumed, but nothing is assumed concerning the dependence between the two possible orientations at any given edge...

We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an edge-cut of size at least 1.33008n, where n is the number of vertices of G, and has fractional cut covering number at most 1.12776. The lower bound on the si...

In this paper we present a study about spanning edge betweenness, an edge-based metric for complex network analysis that is defined as the probability of an edge being part of a minimum spanning tree. This probability reflects how redundant an edge is in what concerns the connectivity of a given network and, hence, its value gives information about the network topology. We apply this metric to ...

Consider a connected undirected graph G with n vertices and m edges, where each edge has some probability p of failing. What is the probability that G becomes disconnected under random, independent edge failures? This can also be viewed as a counting problem, except that each item now has an associated weight: in particular, we want to compute the sum of the weights of all disconnected subgraph...

Banderier, Beier and Mehlhorn [BBM03] showed that the single-source shortest path problem has smoothed complexity w w "| | if the edge costs are -bit integers and the last least significant bits are perturbed randomly. Their analysis holds if each bit is set to or 6 with probability . We extend their result and show that the same analysis goes through for a large class of probability distributi...