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Parameterized Complexity of Diameter

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Algorithms and Complexity (CIAC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11485))

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Abstract

Diameter—the task of computing the length of a longest shortest path—is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no \(O(n^{1.99})\)-time algorithm even in sparse graphs [Roditty and Williams, 2013]. To circumvent this lower bound we aim for algorithms with running time \(f(k) (n+m)\) where k is a parameter and f is a function as small as possible. We investigate which parameters allow for such running times. To this end, we systematically explore a hierarchy of structural graph parameters.

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Notes

  1. 1.

    The h-index of a graph G is the largest number \(\ell \) such that G contains at least \(\ell \) vertices of degree at least \(\ell \).

  2. 2.

    Results marked with (\(\star \)) are deferred to a full version, available under https://arxiv.org/abs/1802.10048.

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Authors and Affiliations

  1. Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany

    Matthias Bentert & André Nichterlein

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  1. Matthias Bentert
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  2. André Nichterlein
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Correspondence to Matthias Bentert .

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  1. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Bentert, M., Nichterlein, A. (2019). Parameterized Complexity of Diameter. In: Heggernes, P. (eds) Algorithms and Complexity. CIAC 2019. Lecture Notes in Computer Science(), vol 11485. Springer, Cham. https://doi.org/10.1007/978-3-030-17402-6_5

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  • DOI: https://doi.org/10.1007/978-3-030-17402-6_5

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