Dynamics-preserving network reductions for ride-pooling paths
Abstract
Reducing the complexity of ride-pooling paths is a central challenge in systems with distributed demand. Here we show that such dynamics admit an exact coarse-grained representation: for a broad class of routing algorithms whose decisions depend only on path lengths, the full network can be reduced to an effective network of active nodes weighted by shortest-path distances without altering the resulting trajectories, up to stochastic degeneracy breaking. The reduction therefore defines an equivalence class of network representations generating identical path dynamics. We further demonstrate that for globally optimizing dispatchers this equivalence is systematically violated through degeneracy amplification, yet remains quantitatively accurate beyond the exactly solvable regime. Our results identify when spatial structure can be integrated out without loss of dynamical fidelity, providing a general framework for the analysis of interacting path processes.
Related
- Separatrix Splitting and Chaotic Dynamics in Collective-Coordinate Reductions of Driven ϕ4 Kinks
- Microscopic description of the fission process including intrinsic excitations. Part III: 240Pu fission dynamics along 1D asymmetric paths within the Schrodinger Collective Intrinsic Model
- Emergence in Network Systems is Bounded by Boundary-Crossing Paths
- Structure-preserving Fourier Neural Operators for Long-time Cahn-Hilliard Dynamics under Coarse Temporal Supervision
- Optimal weight allocation for steering network dynamics to a target time scale
BibTeX
@misc{stiller2026dynamicspreserving,
title = {{Dynamics-preserving network reductions for ride-pooling paths}},
author = {Karolin Stiller and Nora Molkenthin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12603},
eprint = {2609.12603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12603},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamics-preserving network reductions for ride-pooling paths
AU - Karolin Stiller
AU - Nora Molkenthin
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12603
UR - https://arxiv.org/abs/2609.12603
AB - Reducing the complexity of ride-pooling paths is a central challenge in systems with distributed demand. Here we show that such dynamics admit an exact coarse-grained representation: for a broad class of routing algorithms whose decisions depend only on path lengths, the full network can be reduced to an effective network of active nodes weighted by shortest-path distances without altering the resulting trajectories, up to stochastic degeneracy breaking. The reduction therefore defines an equivalence class of network representations generating identical path dynamics. We further demonstrate that for globally optimizing dispatchers this equivalence is systematically violated through degeneracy amplification, yet remains quantitatively accurate beyond the exactly solvable regime. Our results identify when spatial structure can be integrated out without loss of dynamical fidelity, providing a general framework for the analysis of interacting path processes.
ER -