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

Modeling spatial social complex networks for dynamical processes

The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising efficient immunization techniques for the arrest of epidemics, to the design of better transportation and city planning paradigms, to the understanding of how rumors and opinions spread and take shape over time. We develop a spatial social complex network (SSCN) model that captures not only essential connectivity features of real-life social networks, including a heavy-tailed degree distribution and high clustering, but also the spatial location of individuals, reproducing Zipf's law for the distribution of city populations as well as other observed hallmarks. We then simulate Milgram's Small-World experiment on our SSCN model, obtaining good qualitative agreement with the known results and shedding light on the role played by various network attributes and the strategies used by the players in the game. This demonstrates the potential of the SSCN model for the simulation and study of the many social processes mentioned above, where both connectivity and geography play a role in the dynamics.Comment: 10 pages, 6 figure

Walking Through Waypoints

We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set $\mathscr{W}\subseteq V$: the \emph{waypoints}. This waypoint routing problem finds immediate applications in the context of modern networked distributed systems. Our main contribution is an exact polynomial-time algorithm for graphs of bounded treewidth. We also show that if the number of waypoints is logarithmically bounded, exact polynomial-time algorithms exist even for general graphs. Our two algorithms provide an almost complete characterization of what can be solved exactly in polynomial-time: we show that more general problems (e.g., on grid graphs of maximum degree 3, with slightly more waypoints) are computationally intractable

Progressive Simplification of Polygonal Curves

Simplifying polygonal curves at different levels of detail is an important problem with many applications. Existing geometric optimization algorithms are only capable of minimizing the complexity of a simplified curve for a single level of detail. We present an $O(n^3m)$-time algorithm that takes a polygonal curve of n vertices and produces a set of consistent simplifications for m scales while minimizing the cumulative simplification complexity. This algorithm is compatible with distance measures such as the Hausdorff, the Fr\'echet and area-based distances, and enables simplification for continuous scaling in $O(n^5)$ time. To speed up this algorithm in practice, we present new techniques for constructing and representing so-called shortcut graphs. Experimental evaluation of these techniques on trajectory data reveals a significant improvement of using shortcut graphs for progressive and non-progressive curve simplification, both in terms of running time and memory usage.Comment: 20 pages, 20 figure

A Divide-and-Conquer Algorithm for Betweenness Centrality

The problem of efficiently computing the betweenness centrality of nodes has been researched extensively. To date, the best known exact and centralized algorithm for this task is an algorithm proposed in 2001 by Brandes. The contribution of our paper is Brandes++, an algorithm for exact efficient computation of betweenness centrality. The crux of our algorithm is that we create a sketch of the graph, that we call the skeleton, by replacing subgraphs with simpler graph structures. Depending on the underlying graph structure, using this skeleton and by keeping appropriate summaries Brandes++ we can achieve significantly low running times in our computations. Extensive experimental evaluation on real life datasets demonstrate the efficacy of our algorithm for different types of graphs. We release our code for benefit of the research community.Comment: Shorter version of this paper appeared in Siam Data Mining 201

Real-Time Traffic Assignment Using Fast Queries in Customizable Contraction Hierarchies

Given an urban road network and a set of origin-destination (OD) pairs, the traffic assignment problem asks for the traffic flow on each road segment. A common solution employs a feasible-direction method, where the direction-finding step requires many shortest-path computations. In this paper, we significantly accelerate the computation of flow patterns, enabling interactive transportation and urban planning applications. We achieve this by revisiting and carefully engineering known speedup techniques for shortest paths, and combining them with customizable contraction hierarchies. In particular, our accelerated elimination tree search is more than an order of magnitude faster for local queries than the original algorithm, and our centralized search speeds up batched point-to-point shortest paths by a factor of up to 6. These optimizations are independent of traffic assignment and can be generally used for (batched) point-to-point queries. In contrast to prior work, our evaluation uses real-world data for all parts of the problem. On a metropolitan area encompassing more than 2.7 million inhabitants, we reduce the flow-pattern computation for a typical two-hour morning peak from 76.5 to 10.5 seconds on one core, and 4.3 seconds on four cores. This represents a speedup of 18 over the state of the art, and three orders of magnitude over the Dijkstra-based baseline