Dynamically Maintaining Shortest Path Trees under Batches of Updates

D’Andrea, Annalisa; D’Emidio, Mattia; Frigioni, Daniele; Leucci, Stefano; Proietti, Guido

doi:10.1007/978-3-319-03578-9_24

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…Hence, the algorithms we proposed in this work may benefit from any advances made for dynamic shortest path algorithms. For example, recently D'Andrea et al [38] presented an algorithm that allows for dynamically maintaining shortest path trees under batches of updates which can be used by LBT-RRT instead of the SSSP algorithm.…”

Section: Discussionmentioning

confidence: 99%

Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning

2016

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We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1 + ε of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary graph, which we call the lowerbound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRG and RRT*) with little runningtime overhead when compared to RRT.

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Section: Discussionmentioning

confidence: 99%

Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning

2016

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“…For example, recently D'Andrea et al [38] presented an algorithm that allows for dynamically maintaining shortest path trees under batches of updates which can be used by LBT-RRT instead of the SSSP algorithm.…”

Section: Discussionmentioning

confidence: 99%

Asymptotically near-optimal RRT for fast, high-quality, motion planning

Salzman

Halperin

2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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Abstract-We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1 + ε of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary graph, which we call the lowerbound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRG and RRT*) with little runningtime overhead when compared to RRT.

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“…It is imperative to design dynamic algorithms that can efficiently update distance labelling to reflect graph changes for fast and accurate response to distance queries. So far, only limited attempts have been made on maintaining a distance labelling for dynamic graphs [8,10,[24][25][26]. Among them, the methods considering incremental updates (i.e.…”

Section: Introductionmentioning

confidence: 99%

Efficient Maintenance of Highway Cover Labelling for Distance Queries on Large Dynamic Graphs

Farhan

Wang

2022

Preprint

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Graphs in real-world applications are typically dynamic that undergo rapid changes in their topological structure over time by either adding or deleting edges or vertices. However, it is challenging to design algorithms capable of supporting updates efficiently on dynamic graphs. In this paper, we devise a parallel fully dynamic labelling method to reflect changes on graphs for efficient shortest-path distance computation, a fundamental problem in graph theory. At its core, our solution accelerates query processing through a fully dynamic distance labelling with a limited size but providing a good approximation to bound online searches on dynamic graphs. Our parallel fully dynamic labelling method leverages two sources of efficiency gain: landmark parallelism and anchor parallelism. Furthermore, it can handle both incremental and decremental updates efficiently using a unified search approach and a bounded repairing inference mechanism. We theoretically analyze the correctness, labelling minimality and time complexity of our method, and also conduct extensive experiments to empirically verify its efficiency and scalability on 10 real-world large networks.

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Dynamically Maintaining Shortest Path Trees under Batches of Updates

Cited by 11 publications

References 17 publications

Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning

Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning

Asymptotically near-optimal RRT for fast, high-quality, motion planning

Efficient Maintenance of Highway Cover Labelling for Distance Queries on Large Dynamic Graphs

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