Computing Constrained Shortest-Paths at Scale

Motivated by the needs of modern transportation service platforms, we study the problem of computing constrained shortest paths (CSP) at scale via preprocessing techniques. Our work makes two contributions in this regard: 1) We propose a scalable algorithm for CSP queries and show how its performance can be parametrized in terms of a new network primitive, the constrained highway dimension. This development extends recent work that established the highway dimension as the appropriate primitive for characterizing the performance of unconstrained shortest-path (SP) algorithms. Our main theoretical contribution is deriving conditions relating the two notions, thereby providing a characterization of networks where CSP and SP queries are of comparable hardness. 2) We develop practical algorithms for scalable CSP computation, augmenting our theory with additional network clustering heuristics. We evaluate these algorithms on real-world data sets to validate our theoretical findings. Our techniques are orders of magnitude faster than existing approaches while requiring only limited additional storage and preprocessing.

Accelerating exact constrained shortest paths on GPUs

The recently emerging applications such as software-defined networks and autonomous vehicles require efficient and exact solutions for constrained shortest paths (CSP), which finds the shortest path in a graph while satisfying some user-defined constraints. Compared with the common shortest path problems without constraints, CSP queries have a significantly larger number of subproblems. The most widely used labeling algorithm becomes prohibitively slow and impractical. Other existing approaches tend to find approximate solutions and build costly indices on graphs for fast query processing, which are not suitable for emerging applications with the requirement of exact solutions. A natural question is whether and how we can efficiently find the exact solution for CSP. In this paper, we propose Vine , a framework that parallelizes the labeling algorithm to efficiently find the exact CSP solution using GPUs. The major challenge addressed in Vine is how to deal with a large number of subproblems that are mostly unpromising but require a significant amount of memory and computational resources. Our solution is twofold. First, we develop a two-level pruning approach to eliminate the subproblems by making good use of the GPU's hierarchical memory. Second, we propose an adaptive parallelism control model based on the observations that the degree of parallelism (DOP) is the key to performance optimization with the given amount of computational resources. Extensive experiments show that Vine achieves 18× speedup on average over the widely adopted CPU-based solution running on 40 CPU threads. Vine also has over 5× speedup compared with a GPU approach that statically controls the DOP. Compared to the state-of-the-art approximate solution with preprocessed indices, Vine provides exact results with competitive or even better performance.

Modeling and Engineering Constrained Shortest Path Algorithms for Battery Electric Vehicles

We study the problem of computing constrained shortest paths for battery electric vehicles. Because battery capacities are limited, fastest routes are often infeasible. Instead, users are interested in fast routes on which the energy consumption does not exceed the battery capacity. For that, drivers can deliberately reduce speed to save energy. Hence, route planning should provide both path and speed recommendations. To tackle the resulting [Formula: see text]-hard optimization problem, previous work trades correctness or accuracy of the underlying model for practical running times. We present a novel framework to compute optimal constrained shortest paths (without charging stops) for electric vehicles that uses more realistic physical models, while taking speed adaptation into account. Careful algorithm engineering makes the approach practical even on large, realistic road networks: We compute optimal solutions in less than a second for typical battery capacities, matching the performance of previous inexact methods. For even faster query times, the approach can easily be extended with heuristics that provide high quality solutions within milliseconds.