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Solving the MCQP, MLT, and MMLT problems and computing weakly and strongly stable quickest paths

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Abstract

The quickest path problem consists of finding a path in a directed network to transmit a given amount \(\sigma \) of items from a source node to a sink node with minimal transmission time, where the transmission time depends on the traversal times \(\tau \) and the capacities u of the arcs. We suppose that there exist more than one quickest path and finds a quickest path with a special property. In this paper, first, some algorithms to find a quickest path with minimum capacity, minimum lead time, and min-max arc lead time are presented, which runs in \(O(r(m+n \log n))\) and \( O((r(m+n \log n))\log r') \) time, where r and \( r' \) are the number of distinct capacity and lead time values and m and n are the number of arcs and nodes in the given network. Then, we suppose that values \(\sigma , \tau \) and u change to \(\sigma ', \tau '\), and \(u'\). The purpose is to find a quickest path such that it has the minimum transmission time value among all quickest paths, by changing \(\sigma \) to \(\sigma '\), \(\tau \) to \(\tau '\), or u to \(u'\). We show that some of these problems are solved in strongly polynomial time and the others remain as open problems.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran

    Mehdi Ghiyasvand & Azam Ramezanipour

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  1. Mehdi Ghiyasvand
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  2. Azam Ramezanipour
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Correspondence to Mehdi Ghiyasvand.

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Ghiyasvand, M., Ramezanipour, A. Solving the MCQP, MLT, and MMLT problems and computing weakly and strongly stable quickest paths. Telecommun Syst 68, 217–230 (2018). https://doi.org/10.1007/s11235-017-0388-y

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  • DOI: https://doi.org/10.1007/s11235-017-0388-y

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