On a Routing Problem Within Probabilistic Graphs and its Application to Intermittently Connected Networks

Abstract

Given a probabilistic graph G representing an intermittently connected network and routing algorithm A, we wish to determine a delivery subgraph G[A] of G with at most k edges, such that the probability Conn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G[A]) that there is a path from source s to destination t (in a graph H chosen randomly from the probability space defined by G[A]) is maximized. To the best of our knowledge, this problem and its complexity has not been addressed in the literature. Also, there is the corresponding distributed version of the problem where the delivery subgraph G[A] is to be constructed distributively, yielding a routing protocol. Our proposed solution to this routing problem is multi-fold: First, we prove the hardness of our optimization problem of finding a delivery subgraph that maximizes the delivery probability and discuss the hardness of computing the objective function Conn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G[A]); Second, we present an algorithm to approximate Conn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G[A]) and compare it with an optimal algorithm; Third, we focus on intermittently connected networks, and model the users' mobility within them; and Fourth, we propose an edge-constrained routing protocol (EC-SOLAR-KSP) based on the insights obtained from the first step and the contact probabilities computed in the third step. We then highlight the protocol's novelty and effectiveness by comparing it with a probabilistic routing protocol, and an epidemic routing protocol proposed in literature.