Tractable Pathfinding for the Stochastic On-Time Arrival Problem

We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution is a pathfinding algorithm that uses the solution to the policy-based SOTA problem---which is of pseudo-polynomial-time complexity in the time budget of the journey---as a search heuristic for the optimal path. In particular, we show that this heuristic can be exceptionally efficient in practice, effectively making it possible to solve the path-based SOTA problem as quickly as the policy-based SOTA problem. Our secondary contribution is the extension of policy-based preprocessing to path-based preprocessing for the SOTA problem. In the process, we also introduce Arc-Potentials, a more efficient generalization of Stochastic Arc-Flags that can be used for both policy- and path-based SOTA. After developing the pathfinding and preprocessing algorithms, we evaluate their performance on two different real-world networks. To the best of our knowledge, these techniques provide the most efficient computation strategy for the path-based SOTA problem for general probability distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental Algorithms 2016 and published by Springer in the Lecture Notes in Computer Science series on June 1, 2016. Includes typographical corrections and modifications to pre-processing made after the initial submission to SODA'15 (July 7, 2014

Optimization of Free Space Optical Wireless Network for Cellular Backhauling

With densification of nodes in cellular networks, free space optic (FSO) connections are becoming an appealing low cost and high rate alternative to copper and fiber as the backhaul solution for wireless communication systems. To ensure a reliable cellular backhaul, provisions for redundant, disjoint paths between the nodes must be made in the design phase. This paper aims at finding a cost-effective solution to upgrade the cellular backhaul with pre-deployed optical fibers using FSO links and mirror components. Since the quality of the FSO links depends on several factors, such as transmission distance, power, and weather conditions, we adopt an elaborate formulation to calculate link reliability. We present a novel integer linear programming model to approach optimal FSO backhaul design, guaranteeing $K$-disjoint paths connecting each node pair. Next, we derive a column generation method to a path-oriented mathematical formulation. Applying the method in a sequential manner enables high computational scalability. We use realistic scenarios to demonstrate our approaches efficiently provide optimal or near-optimal solutions, and thereby allow for accurately dealing with the trade-off between cost and reliability