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

Allocation in Practice

How do we allocate scarcere sources? How do we fairly allocate costs? These are two pressing challenges facing society today. I discuss two recent projects at NICTA concerning resource and cost allocation. In the first, we have been working with FoodBank Local, a social startup working in collaboration with food bank charities around the world to optimise the logistics of collecting and distributing donated food. Before we can distribute this food, we must decide how to allocate it to different charities and food kitchens. This gives rise to a fair division problem with several new dimensions, rarely considered in the literature. In the second, we have been looking at cost allocation within the distribution network of a large multinational company. This also has several new dimensions rarely considered in the literature.Comment: To appear in Proc. of 37th edition of the German Conference on Artificial Intelligence (KI 2014), Springer LNC

A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.Comment: 6 pages, 3 figure

An Efficient Monte Carlo-based Probabilistic Time-Dependent Routing Calculation Targeting a Server-Side Car Navigation System

Incorporating speed probability distribution to the computation of the route planning in car navigation systems guarantees more accurate and precise responses. In this paper, we propose a novel approach for dynamically selecting the number of samples used for the Monte Carlo simulation to solve the Probabilistic Time-Dependent Routing (PTDR) problem, thus improving the computation efficiency. The proposed method is used to determine in a proactive manner the number of simulations to be done to extract the travel-time estimation for each specific request while respecting an error threshold as output quality level. The methodology requires a reduced effort on the application development side. We adopted an aspect-oriented programming language (LARA) together with a flexible dynamic autotuning library (mARGOt) respectively to instrument the code and to take tuning decisions on the number of samples improving the execution efficiency. Experimental results demonstrate that the proposed adaptive approach saves a large fraction of simulations (between 36% and 81%) with respect to a static approach while considering different traffic situations, paths and error requirements. Given the negligible runtime overhead of the proposed approach, it results in an execution-time speedup between 1.5x and 5.1x. This speedup is reflected at infrastructure-level in terms of a reduction of around 36% of the computing resources needed to support the whole navigation pipeline