Average-Case Behavior of k-Shortest Path Algorithms

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Title: Average-Case Behavior of k-Shortest Path Algorithms
Authors: Schickedanz, Alexander
Ajwani, Deepak
Meyer, Ulrich
Gawrychowski, Pawel
Permanent link: http://hdl.handle.net/10197/9887
Date: 2-Dec-2018
Online since: 2019-04-10T10:58:01Z
Abstract: The k-shortest path problem is a generalization of the fundamental shortest path problem, where the goal is to compute k simple paths from a given source to a target node, in non-decreasing order of their weight. With numerous applications modeling various optimization problems and as a feature in some learning systems, there is a need for efficient algorithms for this problem. Unfortunately, despite many decades of research, the best directed graph algorithm still has a worst-case asymptotic complexity of Õ(k n(n + m)). In contrast to the worst-case complexity, many algorithms have been shown to perform well on small diameter directed graphs in practice. In this paper, we prove that the average-case complexity of the popular Yen’s algorithm on directed random graphs with edge probability p = Ω(log n)/n in the unweighted and uniformly distributed weight setting is O(kmlog n), thus explaining the gap between the worst-case complexity and observed empirical performance. While we also provide a weaker bound of O(kmlog4 n) for sparser graphs with p ≥ 4/n, we show empirical evidence that the stronger bound should also hold in the sparser setting. We then prove that Feng’s directed k-shortest path algorithm computes the second shortest path in expected O(m) time on random graphs with edge probability p = Ω(log n)/n. Empirical evidence suggests that the average-case result for the Feng's algorithm holds even for k > 2 and sparser graphs.
Type of material: Conference Publication
Publisher: Springer
Volume: 812
Start page: 28
End page: 40
Series/Report no.: Studies in Computational Intelligence
Copyright (published version): 2019 Springer
Keywords: k-Shortest path algorithmsAverage case analysisYen’s algorithmFeng’s algorithm
DOI: 10.1007/978-3-030-05411-3_3
Other versions: https://www.2018.complexnetworks.org/
Language: en
Status of Item: Peer reviewed
Is part of: Studies in Computational Intelligence (SCI, volume 812)
Conference Details: The 7th International Conference on Complex Networks and Their Applications, Cambridge, United Kingdom, 11-13 December 2018
ISBN: 9783030054106
Appears in Collections:Computer Science Research Collection

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