An Empirical Comparison of k-Shortest Simple Path Algorithms on Multicores

Ajwani, Deepak; Duriakova, Erika; Hurley, Neil; Meyer, Ulrich; Schickedanz, Alexander

doi:10.1145/3225058.3225075

Cited by 7 publications

(19 citation statements)

References 33 publications

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“…The best k-shortest path algorithm for undirected graphs [21] has a significantly better asymptotic worst-case complexity of O(k(m + n log n)), compared to directed graph algorithms. Despite the big gap between the worst-case asymptotic complexity of directed and undirected graph algorithms, a recent experimental paper [3] showed comparable performance of these algorithms on the random graphs, motivating this theoretical study.…”

Section: Related Workmentioning

confidence: 81%

“…A recent empirical study [3] has found that despite the difference in asymptotics between algorithms for directed and undirected graphs, they are fairly competitive in average on random graphs and that some of the directed graph k-shortest path algorithms scale well on random graphs. We hypothesize that two of the popular directed graph k-shortest simple path algorithms with poor worst-case asymptotic complexity, by Yen [33] and Feng [13], have near-linear average-case asymptotic complexity (explaining their scalability in practice).…”

Section: Introductionmentioning

confidence: 99%

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Average-Case Behavior of k-Shortest Path Algorithms

Schickedanz

Ajwani

Meyer

et al. 2018

Studies in Computational Intelligence

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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 ofÕ(k n(n+m)). In contrast to the worstcase 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(k m log n), thus explaining the gap between the worst-case complexity and observed empirical performance. While we also provide a weaker bound of O(k m log 4 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.

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Section: Related Workmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Average-Case Behavior of k-Shortest Path Algorithms

Schickedanz

Ajwani

Meyer

et al. 2018

Studies in Computational Intelligence

Self Cite

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“…Parallel deviation path identification. Following insights from Para-Yen [28] that parallelized deviation path computation, PYen improves Yen's efficiency by initiating separate search instances to compute spur partial paths from each vertex in P i (s, t) to the destination concurrently. This fully parallelized approach yields speedup over Yen's algorithm, particularly when ample computing resources, such as CPU cores, enable greater parallelism.…”

Section: Pyen Algorithmmentioning

confidence: 99%

“…This fully parallelized approach yields speedup over Yen's algorithm, particularly when ample computing resources, such as CPU cores, enable greater parallelism. In our distributed solution, where computing resources are already stretched with three parallel levels for processing KSP queries, computing partial KSPs, and identifying deviation paths, PYen shifts focus from single shortest path parallelization, as in Para-Yen [28], to optimizing search efficiency by reducing redundant computations and early termination of unpromising deviation path exploration.…”

Section: Pyen Algorithmmentioning

confidence: 99%

Distributed Processing of k Shortest Path Queries over Dynamic Road Networks

Koudas

et al. 2020

Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data

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The problem of identifying the k-shortest paths (KSPs for short) in a dynamic road network is essential to many locationbased services. Road networks are dynamic in the sense that the weights of the edges in the corresponding graph constantly change over time, representing evolving traffic conditions. Very often such services have to process numerous KSP queries over large road networks at the same time, thus there is a pressing need to identify distributed solutions for this problem. However, most existing approaches are designed to identify KSPs on a static graph in a sequential manner (i.e., the (i + 1) t h shortest path is generated based on the i th shortest path), restricting their scalability and applicability in a distributed setting. We therefore propose KSP-DG, a distributed algorithm for identifying k-shortest paths in a dynamic graph. It is based on partitioning the entire graph into smaller subgraphs, and reduces the problem of determining KSPs into the computation of partial KSPs in relevant subgraphs, which can execute in parallel on a cluster of servers.A distributed two-level index called DTLP is developed to facilitate the efficient identification of relevant subgraphs. A salient feature of DTLP is that it indexes a set of virtual paths that are insensitive to varying traffic conditions, leading to very low maintenance cost in dynamic road networks. This is the first treatment of the problem of processing KSP queries over dynamic road networks. Extensive experiments conducted on real road networks confirm the superiority of our proposal over baseline methods.

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“…During the second phase, which involves all the remaining instances, the calculation uses the calculation order defined during the first instance, making the time for calculating a new instance much faster. Several articles have compared different shortest path algorithms for different applications [14,15,16]; however, none of them investigated project schedules. This paper aims to study the characteristics of Algorithms #1-#3 and their modification developed for Monte Carlo simulation (Algorithm #4 a-b) on construction-like networks.…”

Section: Introductionmentioning

confidence: 99%

Project scheduling algorithms for construction projects with stretchable activities

Mályusz

Vattai

2022

IOP Conf. Ser.: Mater. Sci. Eng.

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Project management requires increasingly complex, sophisticated scheduling models, preferably in the simplest possible way, for which the rapid expansion of computing capacity provides an increasing opportunity. In this paper, we examine deterministic models that, as a further development of the traditional CPM and PDM models (with four well-known minimum and maximum priority relationships) allow activity to be stretchable. The aim of the study is a) to implement different algorithms for time analysis on computers, b) to compare their speeds on large-scale real and artificial projects; c) to prepare proposals for selecting the best fitting algorithm(s) to the specific model(s). The comparison was based on real network. The results show that depending on the models, different algorithms perform well, so we recommend that different algorithms be implemented in the scheduling tools and let the tool decide which algorithms will be optimal for the computation time

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An Empirical Comparison of k-Shortest Simple Path Algorithms on Multicores

Cited by 7 publications

References 33 publications

Average-Case Behavior of k-Shortest Path Algorithms

Average-Case Behavior of k-Shortest Path Algorithms

Distributed Processing of k Shortest Path Queries over Dynamic Road Networks

Project scheduling algorithms for construction projects with stretchable activities

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