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Efficient Algorithms for Earliest and Fastest Paths in Public Transport Networks

Mithinti Srikanth, G. Ramakrishna

TL;DR

This work addresses efficient single-source computation of Earliest Arrival Time (EAT) and Fastest Path Duration (FPD) in public transport networks modeled as temporal graphs. It introduces the edge-scan-dependency graph ($\tilde{G}$) and the notion of useful dominating paths to prune exploration, achieving near-linear time $O(m+n)$ through a one-to-one mapping between temporal paths and $\tilde{G}$-paths. The authors provide practical algorithms with CSR-based ES DG implementations, plus GTFS preprocessing, and demonstrate substantial real-world speedups ($\approx$183x for EAT and $\approx$34x for FPD) across nine datasets. These results offer transit planners a scalable and efficient toolkit for route optimization and urban mobility analysis, with clear potential for real-time applications.

Abstract

Public transport administrators rely on efficient algorithms for various problems that arise in public transport networks. In particular, our study focused on designing linear-time algorithms for two fundamental path problems: the earliest arrival time (\textsc{eat}) and the fastest path duration (\textsc{fpd}) on public transportation data. We conduct a comparative analysis with state-of-the-art algorithms. The results are quite promising, indicating substantial efficiency improvements. Specifically, the fastest path problem shows a remarkable 34-fold speedup, while the earliest arrival time problem exhibits an even more impressive 183-fold speedup. These findings highlight the effectiveness of our algorithms to solve \textsc{eat} and \textsc{fpd} problems in public transport, and eventually help public administrators to enrich the urban transport experience.

Efficient Algorithms for Earliest and Fastest Paths in Public Transport Networks

TL;DR

This work addresses efficient single-source computation of Earliest Arrival Time (EAT) and Fastest Path Duration (FPD) in public transport networks modeled as temporal graphs. It introduces the edge-scan-dependency graph () and the notion of useful dominating paths to prune exploration, achieving near-linear time through a one-to-one mapping between temporal paths and -paths. The authors provide practical algorithms with CSR-based ES DG implementations, plus GTFS preprocessing, and demonstrate substantial real-world speedups (183x for EAT and 34x for FPD) across nine datasets. These results offer transit planners a scalable and efficient toolkit for route optimization and urban mobility analysis, with clear potential for real-time applications.

Abstract

Public transport administrators rely on efficient algorithms for various problems that arise in public transport networks. In particular, our study focused on designing linear-time algorithms for two fundamental path problems: the earliest arrival time (\textsc{eat}) and the fastest path duration (\textsc{fpd}) on public transportation data. We conduct a comparative analysis with state-of-the-art algorithms. The results are quite promising, indicating substantial efficiency improvements. Specifically, the fastest path problem shows a remarkable 34-fold speedup, while the earliest arrival time problem exhibits an even more impressive 183-fold speedup. These findings highlight the effectiveness of our algorithms to solve \textsc{eat} and \textsc{fpd} problems in public transport, and eventually help public administrators to enrich the urban transport experience.
Paper Structure (12 sections, 7 theorems, 8 figures, 6 tables)

This paper contains 12 sections, 7 theorems, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Useful Dominating Paths and ESDG
  4. Efficient Algorithm for Fastest Path duration
  5. Implementation Details
  6. Experiments
  7. Performance of the Earliest Arrival Time Algorithm
  8. Performance of the Fastest Path Duration Algorithm
  9. Key Insights
  10. Applications
  11. Related Work
  12. Conclusion

Key Result

lemma 1

If there exists a path from $s$ to $z$ that departs at time $t$ on a route $r$, then there exists a useful dominating path from $s$ to $z$ that starts at time $t$ on the route $r$.

Figures (8)

  • Figure 1: Time spent on chain edges processing in trg based eat algorithm
  • Figure 2: A temporal graph
  • Figure 3: An edge-scan-dependency graph
  • Figure 4: Speed up of Algorithm \ref{['algoEarliestPathVersion2']} w.r.t the state of the art algorithms wu_2016_Fast_EAT_TemporalSahani2021
  • Figure 5: Speed up of Algorithm \ref{['algoFastestPathVersion2']} w.r.t the state of the art algorithms wu_2016_Fast_EAT_TemporalSahani2021
  • ...and 3 more figures

Theorems & Definitions (7)

  • lemma 1
  • corollary 1
  • corollary 2
  • corollary 3
  • lemma 2
  • theorem 1
  • theorem 2