A Probabilistic Divide and Conquer Algorithm for the Minimum Tollbooth Problem

  • Julian NickerlEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11917)


The tollbooth problem aims at minimizing the time lost through congestion in road networks with rational and selfish participants by demanding an additional toll for the use of edges. We consider a variant of this problem, the minimum tollbooth problem, which additionally minimizes the number of tolled edges. Since the problem is NP-hard, heuristics and evolutionary algorithms dominate solution approaches. To the best of our knowledge, for none of these approaches, a provable non-trivial upper bound on the (expected) runtime necessary to find an optimal solution exists.

We present a novel probabilistic divide and conquer algorithm with a provable upper bound of \(\mathcal {O}^*(m^{opt})\) on the expected runtime for finding an optimal solution. Here, m is the number of edges of the network, and opt the number of tolled roads in an optimal solution. Initial experiments indicate that in practice significantly less time is necessary.


Algorithmic game theory Minimum tollbooth problem Network congestion game Social optimum System optimal flow 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceUlm UniversityUlmGermany

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