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Algorithmics for Safe Bicycle Network Design with Bounded Detours in Rural Areas

Author Till Fluschnik

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OASIcs.ATMOS.2026.14.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Theory of computation → Design and analysis of algorithms
  • Social and professional topics → Sustainability
Keywords
  • Parameterized Algorithms
  • NP-hardness
  • Pairwise weighted spanners
  • Preprocessing
  • Integer linear programming
  • Cut generation

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Abstract

We introduce the Safe Bicycle Network with Bounded Detours (SBNBD) problem, a network-design problem motivated by the upgrade of rural road networks for bicycle traffic. Given an undirected graph whose edges have length and are classified as safe or unsafe with unsafe edges carrying upgrade costs, a set of terminal pairs, an upgrade budget, and a detour factor α, the task is to upgrade unsafe edges so that every terminal pair is connected by a safe path whose length is at most α times its shortest-path distance in the original network.
We study the computational complexity of SBNBD from a parameterized perspective. We prove strong NP-hardness even on highly restricted graph classes, including planar graphs of treewidth two, graphs with feedback vertex set number one, and graphs of maximum degree three. We complement these lower bounds with polynomial-time algorithms for trees and graphs of maximum degree two. For parameterized complexity, we show fixed-parameter tractability for the number of unsafe edges and prove matching lower bounds under SETH, a polynomial-kernel lower bound, and W-hardness for natural parameters. Our main positive structural result is an algorithm that maps any instance to an equivalent instance with O(fes+p) vertices and edges, where fes is the feedback edge number and p is the number of terminal pairs; this yields fixed-parameter tractability for the combined parameter fes+p.
Finally, we construct and evaluate exact ILP-based algorithms on road networks derived from OpenStreetMap data for small German municipalities and their surrounding rural regions. The experiments show that these networks have small treewidth upper bounds and moderate feedback edge structure. We introduce a preprocessing routine based on the reduction algorithm for the parameter fes+p and a heuristic cut generation based on tree decompositions. Both improve exact solving performance, in particular for harder instances. Our results for different detour-factor bounds show that a moderate increase in α can substantially reduce the total length of the upgraded network, revealing practical trade-offs between upgrade budget and the maximum allowed relative detour. Our results indicate that structural graph parameters provide a useful algorithmic lens for safe bicycle-network design in rural areas.

Cite As Get BibTex

Till Fluschnik. Algorithmics for Safe Bicycle Network Design with Bounded Detours in Rural Areas. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/OASIcs.ATMOS.2026.14

Author Details

Till Fluschnik
  • Department of Computer Science, Algorithm Engineering Group, Humboldt-Universität zu Berlin, Germany

Funding

  • Fluschnik, Till: Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project PACS (FL 1247/1-1, 522475669).

Supplementary Materials

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