Computing Constrained Shortest-Paths at Scale

• Published in: Operations research Vol. 70; no. 1; pp. 160 - 178
• Main Authors: Vera, Alberto, Banerjee, Siddhartha, Samaranayake, Samitha
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.01.2022; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Cloud computing; Clustering; Computation; constrained shortest path; distance oracles; highway dimension; Mathematical models; Network flow problem; Operations research; Preprocessing; Queries; Shortest path algorithms; Shortest-path problems; Transportation; Transportation services
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.2021.2166

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. 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.