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International Conference on Computational Data and Social Networks

CSoNet 2019: Computational Data and Social Networks pp 3–15Cite as

A Probabilistic Divide and Conquer Algorithm for the Minimum Tollbooth Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11917))

Abstract

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.

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, Ulm University, Ulm, Germany

    Julian Nickerl

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  1. Julian Nickerl
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Correspondence to Julian Nickerl .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Andrea Tagarelli

  2. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Hanghang Tong

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Nickerl, J. (2019). A Probabilistic Divide and Conquer Algorithm for the Minimum Tollbooth Problem. In: Tagarelli, A., Tong, H. (eds) Computational Data and Social Networks. CSoNet 2019. Lecture Notes in Computer Science(), vol 11917. Springer, Cham. https://doi.org/10.1007/978-3-030-34980-6_1

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  • DOI: https://doi.org/10.1007/978-3-030-34980-6_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34979-0

  • Online ISBN: 978-3-030-34980-6

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