On the quickest path problem

Hung, Yung-Chen; Chen, Gen-Huey

doi:10.1007/3-540-54029-6_152

Cited by 13 publications

(7 citation statements)

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“…The quickest path problem [2] is a restricted version of MTT by requiring the transmission of data to be done along a single path from the source to the destination (i.e., no partition of data is required). This requirement makes the problem solvable in polynomial time [2,9,11]. The computation of a quickest path differs in many aspects from the computation of the related shortest path.…”

Section: Restricting Mtt: the Quickest Path Problemmentioning

confidence: 99%

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Transmissions in a network with capacities and delays

et al. 1999

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We examine the problem of transmitting in minimum time a given amount of data between a source and a destination in a network with finite channel capacities and nonzero propagation delays. In the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we show that the general problem is NP‐complete. In addition, we examine transmissions along a single path, called the quickest path, and present algorithms for general and special classes of networks that improve upon previous approaches. The first dynamic algorithm for the quickest path problem is also given. © 1999 John Wiley & Sons, Inc. Networks 33: 167–174, 1999

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Section: Restricting Mtt: the Quickest Path Problemmentioning

confidence: 99%

“…For sparse networks [i.e., m ϭ O(n)], this complexity becomes O(rn log n). The all-pairs quickest path problem has been solved in O(min{rnm ϩ rn 2 log n, mn 2 }) time [9], which for sparse networks becomes O(min{rn 2 log n, n 3 }).…”

Section: Introductionmentioning

confidence: 99%

Transmissions in a network with capacities and delays

et al. 1999

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“…This requirement makes the problem solvable in polynomial time [1,8,10]. The computation of a quickest path differs in many aspects from the computation of the related shortest path.…”

Section: Restricting Mtt: the Quickest Path Problemmentioning

confidence: 99%

“…In particular, the best previous algorithm for the single-pair quickest path problem runs in time O(rm + rn log n) [1,10], where r is the number of distinct edge capacities. The all-pairs quickest path problem has been solved in O(min{rnm + rn 2 log n, mn 2 }) time [8].…”

Section: Introductionmentioning

confidence: 99%

On the computation of fast data transmissions in networks with capacities and delays

Kagaris¹,

Tragoudas²,

Pantziou

et al. 1995

Lecture Notes in Computer Science

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Abstract. We examine the problem of transmitting in minimum time a given amount of data between a source and a destination in a network with finite channel capacities and non-zero propagation delays. In the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we show that the general problem is NP-hard. In addition, we examine transmissions along a single path, called the quickest path, and present algorithms for general and sparse networks that outperform previous approaches. The first dynamic algorithm for the quickest path problem is also given.

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“…Other authors also derived polynomial‐time algorithms for this problem [12, 17]. Numerous variants and extensions of the quickest path problem have been considered, including all pairs quickest path problems [8, 10], the k ‐quickest path problem [3], and most reliable quickest path problems [11, 19]. More information about quickest path problems can be found in the survey of Pascoal et al [16].…”

Section: Introductionmentioning

confidence: 99%

Min‐Max quickest path problems

Ruzika

Thiemann

2012

Networks

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In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time. In practical settings, for example in evacuation or transportation planning, the problem parameters might not be known exactly a-priori. It is therefore of interest to consider robust versions of these problems in which travel times and/or capacities of arcs depend on a certain scenario. In this article, min-max versions of robust quickest path problems are investigated and, depending on their complexity status, exact algorithms or fully polynomial-time approximation schemes are proposed.

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On the quickest path problem

Cited by 13 publications

References 1 publication

Transmissions in a network with capacities and delays

Transmissions in a network with capacities and delays

On the computation of fast data transmissions in networks with capacities and delays

Min‐Max quickest path problems

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