Journal of Combinatorial Optimization

, Volume 36, Issue 1, pp 131–141 | Cite as

Approximation algorithms for the bus evacuation problem

  • Lehilton L. C. Pedrosa
  • Rafael C. S. Schouery


We consider the bus evacuation problem. Given a positive integer B, a bipartite graph G with parts S and \(T \cup \{r\}\) in a metric space and functions \(l_i :S \rightarrow {\mathbb {Z}}_+\) and \({u_j :T \rightarrow \mathbb {Z}_+ \cup \{\infty \}}\), one wishes to find a set of B walks in G. Every walk in B should start at r and finish in T and r must be visited only once. Also, among all walks, each vertex i of S must be visited at least \(l_i\) times and each vertex j of T must be visited at most \(u_j\) times. The objective is to find a solution that minimizes the length of the longest walk. This problem arises in emergency planning situations where the walks correspond to the routes of B buses that must transport each group of people in S to a shelter in T, and the objective is to evacuate the entire population in the minimum amount of time. In this paper, we prove that approximating this problem by less than a constant is \(\text{ NP }\)-hard and present a 10.2-approximation algorithm. Further, for the uncapacitated BEP, in which \(u_j\) is infinity for each j, we give a 4.2-approximation algorithm.


Bus evacuation Emergency planning Approximation algorithm 



Supported by Grant #2015/11937-9, São Paulo Research Foundation (FAPESP) and Grants #425340/2016-3, #308689/2017-8 and #313026/2017-3, National Council for Scientific and Technological Development (CNPq).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of ComputingUniversity of CampinasCampinasBrazil

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