Esther Yizhen. Chua · DR-NTU (Nanyang Technological University) · 2011
Shortest path problem is a problem that is relevant to a wide range of applications like traffic simulation and network routing. These applications play a huge part in our daily lives thus there is a need to explore algorithms which are faster and more efficient. \n \nThis project explores and implements Dijkstra’s algorithm and Transit algorithm. \n \nDijkstra’s algorithm is an algorithm that computes the shortest path between two nodes in a graph whose path costs are positive by iteratively visiting all the nodes that are closer to the source than the destination before eventually reaching the destination. \n \nTransit algorithm makes use of transit nodes as a mean to pre-process a road network where transit nodes are a set of nodes with the property that every non-local shortest path passes through at least one of these nodes. A path is deemed as non-local if its source and destination are more than 4 grid cells apart. \n \nComputation of the length of the shortest paths between each pair of transit nodes and between each node in the graph and its neighboring transit nodes are done thus allowing non-local shortest path queries to be answered in an extremely fast manner by combining information from a small number of lookup in a table. \n \nDijkstra’s algorithm, on average will take seconds for a random query while Transit algorithm is expected to have a worst case query processing time of about 10 microseconds for 99% of the queries on United States network which has around 24 million nodes and 29 million edges.
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RAJAT SHARMA(13BCE · 2015
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ANUBHAV KUMAR PRASAD, ARUNI SINGH · Zenodo (CERN European Organization for Nuclear Research) · 2025
Abstract Success of min heap is because of its typical structure with parents containing values smaller than their children which makes them faster for sorting n elements in n time. This motivated Dijkstra to implement its ‘single source shortest path’ algorithm using min heap. However, one drawback of the min heap is its self-destructive nature that has been used in the algorithms of heapsort and priority queues. There is one variant of heap known as Fibonacci heap which is best suited for Dijkstra’s algorithm. In the case of the heapsort algorithm, the elements are removed from the min heap one by one which destroy the min heap making it impossible to perform any operation on it which restricts Dijkstra’s algorithm in detecting a negative weight cycle. The self-destructive nature of min heap inspired to introduce a novel structure named as Enhanced Heap to resolve the issue of self-destruction without any extra overhead.
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Daniel R. Lanning, Gregory K. Harrell, Jin Wang · 2014
Dijkstra's Algorithm is known as the shortest path source. In this paper, we discuss this Algorithm and the applications that the algorithm has on the modern day. In this study, we provide a pseudo-code of the algorithm. It is the backbone of every navigation system. Google Maps is a typical application of this Algorithm.
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Tetiana Shestakevych · Open Research Knowledge Graph (ORKG) · 2024
The review highlights case studies demonstrating the algorithm's applicability in real-time systems. Based on Scopus indexed papers from 2022 to 2024.
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Wisse van der Meulen, Mark D. Timmer · University of Twente Research Information · 2022
Voor zijn afstudeeropdracht voor de eerstegraads lerarenopleiding aan de Universiteit Twente ontwikkelde Wisse van der Meulen een lessenserie over grafentheorie en het algoritme van Dijkstra voor 4/5 vwo wiskunde B. Dit algoritme wordt gebruikt voor het vinden van kortste/snelste routes. Samen met zijn afstudeerbegeleider, Mark Timmer, bespreekt hij de belangrijkste resultaten.
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Singh, Yash, Trehan, Lakshay · Zenodo (CERN European Organization for Nuclear Research) · 2025
In this project, we address the optimization challenge of flight route planning within a given network of airports, emphasizing scenarios where direct flights are unavailable. The primary objective is to find the shortest path, considering factors such as flight distance or time, between a specified source and destination airport. By constructing a weighted graph that represents the flight network and applying Dijkstra's algorithm, we aim to provide an efficient solution for route planning, essential for minimizing travel time and operational costs in the aviation industry.
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Singh, Yash, Trehan, Lakshay · Zenodo (CERN European Organization for Nuclear Research) · 2025
In this project, we address the optimization challenge of flight route planning within a given network of airports, emphasizing scenarios where direct flights are unavailable. The primary objective is to find the shortest path, considering factors such as flight distance or time, between a specified source and destination airport. By constructing a weighted graph that represents the flight network and applying Dijkstra's algorithm, we aim to provide an efficient solution for route planning, essential for minimizing travel time and operational costs in the aviation industry.
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Gintaras Vaira, Olga Kurasova · Frontiers in artificial intelligence and applications · 2011
This paper deals with Dijkstra's shortest path algorithm and with the possibilities of speeding-up this algorithm. This algorithm is a breadth-first-search algorithm. The search spreads circularly around the source node in order to find the shortest path from the source node to other nodes. Each following iteration is based on the results of the previous iteration, therefore parallelization of such an algorithm is complicated. The parallel Dijkstra algorithm, proposed in this paper, is based on the bidirectional Dijkstra algorithm and popular multicore technology. Such a technology enables to create a parallel algorithm based on the shared memory and most of the time for data synchronization thereby is saved. The proposed algorithm has been tested using the real road network data. The proposed parallel algorithm is almost 3 times faster than the standard Dijkstra algorithm.
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Muhammad Ahsan Khan · SSRN Electronic Journal · 2023
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J. O. Olusina, J. B. Olaleye · Nigerian Journal of Environmental Sciences and Technology · 2017
This paper describes some benefits of crime mapping in a Geographic Information Systems (G.I.S.) environment. The underlining principle of Journey to Crime was discussed. Crime Spots and Police Stations in the study area were mapped, Shortest-Path, Closest Facility, Service Area and OD (Origin – Destination) Cost Matrix were determined based on Dijkstra's Algorithm. Results show that the distribution of police stations does not correspond with the spread of crime spots.
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Shlomi Dolev, Ted Herman · ArXiv.org · 2001
The first self-stabilizing algorithm [Dij73] assumed the existence of a central daemon, that activates one processor at time to change state as a function of its own state and the state of a neighbor. Subsequent research has reconsidered this algorithm without the assumption of a central daemon, and under different forms of communication, such as the model of link registers. In all of these investigations, one common feature is the atomicity of communication, whether by shared variables or read/write registers. This paper weakens the atomicity assumptions for the communication model, proposing versions of [Dij73] that tolerate various weaker forms of atomicity. First, a solution for the case of regular registers is presented. Then the case of safe registers is considered, with both negative and positive results presented. The paper also presents an implementation of [Dij73] based on registers that have probabilistically correct behavior, which requires a notion of weak stabilization.
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Andreas Crauser, Kurt Mehlhorn, Ulrich Meyer et al. · Max Planck Institute for Plasma Physics · 1998
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Jordi Ros-Giralt, Alan Commike, Peter Cullen et al. · 2018
Multiresolution priority queues are recently introduced data structures that can trade-off a small bounded error for faster performance. When used to implement the frontier set in label setting algorithms, they provide a new mathematical approach to classic graph problems such as the computation of shortest paths or minimum spanning trees. To understand how they work, this paper presents a mathematical study of multiresolution label setting algorithms. The theory is general in that the classic mathematical results respond to the particular case where the problem's resolution is infinitely small. The concept of multiresolution helps break the information theoretic barriers of the problem by achieving lower time complexity at the cost of introducing a bounded error. Such error is proven independent of the graph size, a relevant feature in uniform-cost search algorithms where graphs can be infinitely large. Properly tuned, Dijkstra's multiresolution algorithm delivers an amortized cost of O(|V|+|E|), where V and E are the set of vertices and edges, respectively. Benchmarks show speedups of 53% and 26% when applied to Dijkstra's and A* algorithms on a graph of US roads with 87,575 vertices and 121,961 edges.
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J.T. Economou, Georgios P. Kladis, Antonios Tsourdos et al. · 2007
Unmanned aerial vehicles (UAV) are becoming more autonomous, rapidly sophisticated and intelligent due to the large on-board computer power, control algorithms and sensor systems. In the research literature there is a plethora of work, which addresses systematically among other issues the UAV path planning process. Very little work however, addresses the complementary step for satisfying the on-board UAV energy constraints. In this paper, the path planning has been considered as a priori, and therefore results in a choice of optimum paths to be utilised. These optimum paths correspond to the minimum travelling ranges. In practice, aerodynamic effects such as wind disturbances on the UAV, can alter the corresponding energies of these paths. Hence in this paper the Euclidean paths are mapped to energy costs. The proposed problem setting, is solved together with the 4-zone strategy using Dijkstra's Algorithm. The effectiveness for the proposed methodology is shown by a multi-scenario approach.
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Möhring, Rolf H., Schilling, Heiko, Schütz, Birk et al. · DepositOnce · 2005
In this paper, we consider Dijkstra's algorithm for the point-to-point shortest path problem in large and sparse graphs with a given layout. Lauther presented a method that uses a partitioning of the graph to perform a preprocessing which allows to speed-up Dijkstra's algorithm considerably. We present an experimental study that evaluates which partitioning methods are suited for this approach. In particular, we examine partitioning algorithms from computational geometry and compare their impact on the speed-up of the shortest-path algorithm. Using a suited partitioning algorithm speed-up factors of 500 and more were achieved. Furthermore, we present an extension of this speed-up technique to multiple levels of partitionings. With this multi-level variant, the same speed-up factors can be achieved with smaller space requirements. It can therefore be seen as a compression of the precomputed data that conserves the correctness of the computed shortest paths.
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Wenzhi Chen · 2016
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Artturi Tilanterä, Juha Sorva, Otto Seppälä et al. · 2024
Teachers who are aware of potential student misconceptions teach better than teachers who do not. In this article, we focus on misconceptions in the context of teaching and learning graph algorithms: we seek to discover student misconceptions about Dijkstra’s shortest-path algorithm and related concepts. We observed and interviewed fourteen students who worked on a visual simulation task involving the algorithm; we qualitatively analyzed these data to explore the students’ mistakes and their underlying reasons. We find, among other things, that students conflate concepts such as spanning tree, fringe, and priority queue and that students may neglect the greedy and dynamic-programming aspects of the algorithm; we also identify usability issues in the visualization tool we employed. These findings suggest that teachers and tool designers need to take great care to help students tease apart the key concepts in graph algorithms.
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Artturi Tilanterä, Ari Korhonen, Otto Seppälä et al. · Aaltodoc (Aalto University) · 2025
This full research paper explores undergraduate students' misconceptions of Dijkstra's algorithm quantitatively. Graph algorithm misconceptions have been studied to a modest extent, but they support effective instruction. A visual algorithm simulation (VAS) exercise requires a student to trace the algorithm by modifying a data structure visualization. We investigated effective ways to mine new algorithm misconceptions from VAS exercise data. In addition, we searched for previously unknown misconceptions of Dijkstra's algorithm. Students simulated Dijkstra's algorithm with a VAS exercise by adding edges of a given graph to a spanning tree. The simulations produced execution patterns which were mapped into a canonical form. We constructed another graph representing exercise states in all simulations. Using an interactive visualization of the state graph, we built hypotheses for misconceptions. The hypotheses were modeled as algorithms whose execution patterns were matched against students' simulations to find frequency of the hypothetical misconceptions. Pattern matching indicated that certain simulations resembled depth-first search, breadth-first search, and Prim's algorithm. Other simulations had evidence that students had understood the purpose of Dijkstra's algorithm, but arrived to the correct solution with ad hoc heuristics. The findings demonstrate how a VAS exercise was designed to reveal students' difficulties with graph algorithms. The methodology supports recognizing common misconceptions and therefore giving automated, formative feedback. The misconceptions itself are applicable to any exercise on elementary graph algorithms. Interactive visualization of an exercise state graph demonstrates the use of a new data-driven method for eliciting misconceptions.
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O.O. Arhipova, A.N. Kaplunov, L.YU. SHevyrev · 2021
This article discusses the solution of the transport problem using the "Dijkstra algorithm" to determine the shortest routes of transportation. The transport problem is solved for intra-city routes.
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