A Survey of Shortest-Path Algorithms

Madkour, Loutfy H.; Aref, Walid G.; Rehman, Faizan ur; Rahman, Mohamed Abdur; Basalamah, Saleh

doi:10.48550/arxiv.1705.02044

Cited by 13 publications

(15 citation statements)

References 108 publications

(128 reference statements)

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“…A wide variety of shortest path problems have been studied extensively with many efficient solutions [see 22,33]. A particularly useful setting is to model the network with temporal data that brings time savings for the average journey [10].…”

Section: Related Workmentioning

confidence: 99%

Collective shortest paths for minimizing congestion on temporal load-aware road networks

Conlan

Cunningham

Demirci

et al. 2021

Proceedings of the 14th ACM SIGSPATIAL International Workshop on Computational Transportation Science

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Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network) and their execution dynamically affects other queries and network parameters, such as the loads on edges, which in turn affects the shortest paths. We study the problem of collectively processing shortest path queries, where the objective is to optimize a collective objective, such as minimizing the overall cost. We define a temporal load-aware network that dynamically tracks expected loads while satisfying the desirable 'first in, first out' property. We develop temporal load-aware extensions of widely used shortest path algorithms, and a scalable collective routing solution that seeks to reduce system-wide congestion through dynamic path reassignment. Experiments illustrate that our collective approach to this NP-hard problem achieves improvements in a variety of performance measures, such as, i) reducing average travel times by up to 63%, ii) producing fairer suggestions across queries, and iii) distributing load across up to 97% of a city's road network capacity. The proposed approach is generalizable, which allows it to be adapted for other concurrent query processing tasks over networks.

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Section: Related Workmentioning

confidence: 99%

Collective shortest paths for minimizing congestion on temporal load-aware road networks

Conlan

Cunningham

Demirci

et al. 2021

Proceedings of the 14th ACM SIGSPATIAL International Workshop on Computational Transportation Science

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“…Intuitively, the reach of a vertex encodes the lengths of shortest paths on which it lies, and can be used in combination with the A * algorithm to compute shortest paths. An extensive survey of combinatorial algorithms to solve the shortest path problem is given by Madkour et al [20]. However, there has also been great interest from the field of ML in finding approximates for the shortest path distance, using a ML perspective.…”

Section: Related Workmentioning

confidence: 99%

Dijkstras algorithm with predictions to solve the single-source many-targets shortest-path problem

Feijen¹,

Schäfer²

2021

Preprint

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We study the use of machine learning techniques to solve a fundamental shortest path problem, which is also known as the single-source many targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to compute a shortest path from a given source node to any of several designated target nodes. Basically, our idea is to combine a machine learning approach with an adapted version of Dijkstra's algorithm to solve this problem: Based on the trace of Dijkstra's algorithm, we design a neural network that predicts the shortest path distance after only a few iterations. The prediction is then used to prune the search space explored by Dijkstra's algorithm, which allows us to save a significant fraction of operations on the underlying priority queue. Crucially, our approach always computes the exact shortest path distances, even if the prediction is inaccurate, and never uses more queue operations than the standard algorithm. In fact, we are able to prove a lower bound on the number of queue operations saved by our new algorithm, which depends on the accuracy of the prediction. Our bound applies to arbitrary graphs as long as (some of) the edge weights are drawn at random. Our experimental findings on random graphs confirm these bounds and show that the actual savings are oftentimes significantly higher.

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“…We note that (i) this is a deterministic worst-case bound that (ii) does not make any assumptions about the structure of the network, and (iii) the underlying algorithm offers an exponential improvement over Dijkstra's algorithm. There also exist speed-up techniques for road networks that are suitable for real-time implementations (see, e.g., [25] and references therein). For (v, c) pairs that require charging, the shortest path from the vehicle to the location of the customer consists of a shortest path from the vehicle to a charging station (already determined by the SSSP for all nodes in V S ) and then a shortest path from the charging station to the customer.…”

Section: Network Constructionmentioning

confidence: 99%

A Real-Time Dispatching Strategy for Shared Automated Electric Vehicles with Performance Guarantees

Li,

Pantelidis,

Chow

et al. 2020

Preprint

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Car-sharing has emerged as a competitive technology for urban mobility. Combined with the upward trend in vehicle electrification and the promise of automation, it is expected that urban travel will change in fundamental ways in the near future. Indeed, breakthroughs in battery technology and the incentive programs offered by governments worldwide have resulted in a continued increase in the market share of electric vehicles. Automation frees passengers from having to drive and seek parking, it also offers increased flexibility when selecting pick up locations. These trends and incentives naturally suggest that shared automated electric vehicle (SAEV) systems will displace traditional gasoline-powered, human-driven car-sharing systems worldwide.Real-time vehicle dispatching operations in traditional car-sharing systems is an already computationally challenging scheduling problem. Electrification only exacerbates the computational difficulties as charge level constraints come into play. To overcome this complexity, we employ an online minimum drift plus penalty (MDPP) approach for SAEV systems that (i) does not require a priori knowledge of customer arrival rates to the different parts of the system (i.e. it is practical from a real-world deployment perspective), (ii) ensures the stability of customer waiting times, (iii) ensures that the deviation of dispatch costs from a desirable dispatch cost can be controlled, and (iv) has a computational timecomplexity that allows for real-time implementation. Using an agent-based simulator developed for SAEV systems, we test the MDPP approach under two scenarios with real-world calibrated demand and charger distributions: 1) a low-demand scenario with long trips, and 2) a high-demand scenario with short trips. The comparisons with other algorithms under both scenarios show that the proposed online MDPP outperforms all other algorithms in terms of both reduced customer waiting times and vehicle dispatching costs.

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A Survey of Shortest-Path Algorithms

Cited by 13 publications

References 108 publications

Collective shortest paths for minimizing congestion on temporal load-aware road networks

Collective shortest paths for minimizing congestion on temporal load-aware road networks

Dijkstras algorithm with predictions to solve the single-source many-targets shortest-path problem

A Real-Time Dispatching Strategy for Shared Automated Electric Vehicles with Performance Guarantees

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