On the Bike Spreading Problem

Authors Elia Costa, Francesco Silvestri

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Author Details

Elia Costa
  • Dept. of Information Engineering, University of Padova, Italy
Francesco Silvestri
  • Dept. of Information Engineering, University of Padova, Italy


The authors would like to thank the Municipality of Padova for providing us the dataset with rides of the free-floating service in Padova. We are also grateful to Pietro Rampazzo for providing us the grids of the city of Padova and useful suggestions on plotting maps.

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Elia Costa and Francesco Silvestri. On the Bike Spreading Problem. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


A free-floating bike-sharing system (FFBSS) is a dockless rental system where an individual can borrow a bike and returns it anywhere, within the service area. To improve the rental service, available bikes should be distributed over the entire service area: a customer leaving from any position is then more likely to find a near bike and then to use the service. Moreover, spreading bikes among the entire service area increases urban spatial equity since the benefits of FFBSS are not a prerogative of just a few zones. For guaranteeing such distribution, the FFBSS operator can use vans to manually relocate bikes, but it incurs high economic and environmental costs. We propose a novel approach that exploits the existing bike flows generated by customers to distribute bikes. More specifically, by envisioning the problem as an Influence Maximization problem, we show that it is possible to position batches of bikes on a small number of zones, and then the daily use of FFBSS will efficiently spread these bikes on a large area. We show that detecting these zones is NP-complete, but there exists a simple and efficient 1-1/e approximation algorithm; our approach is then evaluated on a dataset of rides from the free-floating bike-sharing system of the city of Padova.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Approximation algorithms analysis
  • Information systems → Data mining
  • Mobility data
  • bike sharing
  • bike relocation
  • influence maximization
  • NP-completeness
  • approximation algorithm


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