Ran Duan, Xiao Mao, Xinkai Shu et al. · ArXiv.org · 2026
This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log \log n})$ for sparse graphs. This improves the recent breakthrough result of $O(m\log^{2/3} n)$ time for directed SSSP algorithm [Duan, Mao, Mao, Shu, Yin 2025].
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Ran Duan, Xiao Mao, Xinkai Shu et al. · arXiv (Cornell University) · 2026
This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log \log n})$ for sparse graphs. This improves the recent breakthrough result of $O(m\log^{2/3} n)$ time for directed SSSP algorithm [Duan, Mao, Mao, Shu, Yin 2025].
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Zhenghao Xi, Heping Liu, Huaping Liu et al. · The Scientific World JOURNAL · 2014
To solve the persistently multiple object tracking in cluttered environments, this paper presents a novel tracking association approach based on the shortest path faster algorithm. First, the multiple object tracking is formulated as an integer programming problem of the flow network. Then we relax the integer programming to a standard linear programming problem. Therefore, the global optimum can be quickly obtained using the shortest path faster algorithm. The proposed method avoids the difficulties of integer programming, and it has a lower worst-case complexity than competing methods but better robustness and tracking accuracy in complex environments. Simulation results show that the proposed algorithm takes less time than other state-of-the-art methods and can operate in real time.
Cited by 9Open access
Tadao Takaoka · Lecture notes in computer science · 2004
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James B. Orlin, Kamesh Madduri, K. Subramani et al. · Journal of Discrete Algorithms · 2009
Cited by 79Open access
Matthew Williamson · 2009
This thesis proposes an algorithm that involves Dijkstra's algorithm to solve the Single Source Shortest Path Problem in a graph where the length of each edge is positive, and the specific case where there is a distinct number of possible lengths. Given a graph where there are n vertices, m edges, and K distinct edge lengths, the proposed algorithm runs in O(m ) time if nK ≤ 2m and O(m log nKm ) time if nK > 2m. The algorithm is tested and compared with some of the fastest algorithms for the Single Source Shortest Path Problem for graphs with arbitrary lengths. The results verify the theoretical conclusions that the proposed algorithm is better, in the case where K is small, than the compared algorithms that did not take advantage of having few distinct edge lengths.
Cited by 11Open access
QIU Wei-jiang, SONG Zhi-qiang, YUAN Jia-bin · SHILAP Revista de lepidopterología · 2013
In view of problem of low efficiency of path planning for mobile robot, an optimal path planning method for mobile robot based on improved shortest path faster algorithm was proposed. On the basis of rules, the method addes start point and terminal point to Voronoi diagram with obstacles, so as to obtain non-collision path graph, then uses the improved shortest path faster algorithm to search an optimal non-collision path between the start point and the terminal point. The simulation result shows that the mobile robot can reach the terminal point rapidly along with the optimal non-collision path by use of the improved algorithm.
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Tatsuya Ohshima · 2008
The shortest path problem is one of the most classical problem in combinatorial optimization problem which, given an edge-weighted graph and two vertices, asks to find a path between the two vertices of the minimum length. In this thesis, we consider a generalization of the shortest path problem in which the edge length is time-variable, which we call the time-dependent shortest path problem. This kind of problems has many applications in the fields of navigation systems and others. Since the first algorithm was proposed by Cooke and Halsey in 1966, many studies have been done for this problem. Currently the fastest algorithm is due to Dreyfus and others (1969–1990) who proposed a straightforward generalization of the famous Dijkstra algorithm that is originally developed for the classical shortest path problem. In this thesis, we give an even faster algorithm at a small amount of extra preprocessing cost. The proposed algorithm is based on the ALT algorithm proposed by Goldberg and Harrelson (2005) for the shortest path problem, in which the main idea is to use pre-calculated landmarks in determining the interim distance labels for vertices. Experimental results show our algorithms is several times faster than the generalized Dijkstra algorithm.
Cited by 2
Neal E. Young, Robert E. Tarjan, James B. Orlin · 1991
We use Fibonacci heaps to improve a parametric shortest path algorithm of Karp and Orlin, and we combine our algorithm and the method of Schneider and Schneider’s minimum-balance algorithm to obtain a faster minimum-balance algorithm. For a graph with n vertices and m edges, our parametric shortest path algorithm and our minimum-balance algorithm both run in O(nm + n 2 log n) time, improved from O(nm log n) for the parametric shortest path algorithm of Karp and Orlin and O(n 2 m) for the minimum-balance algorithm of Schneider and Schneider. An important application of the parametric shortest path algorithm is in finding a minimum mean cycle. Experiments on random graphs suggest that the expected time for finding a minimum mean cycle with our algorithm is O(n log n + m). 1
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Zhi-wang Jiang, Hongxia Zhang · Advances in computer science research · 2015
The shortest path problem is a classical problem in graph theory, it is also one of the classical problems in the field of combinatorial optimization. This paper analyzes the basic harmony search algorithm model, and points out its insufficiency in solving the shortest path problem, then modifies the harmony memory and perturbation method. The simulation experiment shows that the improved harmony search algorithm (IHSA) has faster global convergence speed, and can obtain more accurate optimal path. IHSA is an effective solution to solve the shortest path problem.
Cited by 4Open access
Johnson · ODU Digital Commons (Old Dominion University) · 2016
Domain decomposition is a divide-and-conquer strategy. In the first part of this dissertation, a new/simple/efficient domain decomposition partitioning algorithm is proposed to break a large domain into smaller sub-domains, in such a way as to minimize the number of system boundary nodes and to balance the work load for each sub-domain. This new domain decomposition algorithm is based on the network’s shortest path solution. Numerical results indicate that the new Shortest Distance Decomposition Algorithm outperformed the most widely used METIS algorithm in 21 out of 27 tested (transportation) examples. In the second part of this dissertation, another new/simple and highly efficient shortest path algorithm is described for finding the shortest path from all-to-all (all source nodes to all destination nodes). This new Domain Decomposition-based Shortest Path algorithm basically finds the SP from all-to-all for each sub-domain, and assembles each sub-domains’ shortest path solution to correctly obtain the original (un-partitioned) network’s shortest path solution. Numerical results for real-life transportation networks have shown that the algorithm is much faster than the existing Dijkstra’s shortest path algorithm. Finally, the Shortest Distance Decomposition Algorithm has also been shown to perform better than METIS when minimizing the non-zero fill-in terms of structural engineering stiffness matrices used during the finite element simultaneous linear equation solution process.
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Jinzuo Guo, Hongbin Liu, Tianyu Liu et al. · Mathematics · 2024
The optimization of emergency logistical transportation is crucial for the timely dispatch of aid and support to affected areas. By incorporating practical constraints into emergency logistics, this study establishes a multi-objective shortest path mixed-integer programming model based on a multimodal transportation network. To solve multi-objective shortest path problems with multimodal transportation, we design an ideal point method and propose a procedure for constructing the complete Pareto frontier based on the k-shortest path multi-objective algorithm. We use modified Dijkstra and Floyd multimodal transportation shortest path algorithms to build a k-shortest path multi-objective algorithm. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments carried out on test sets of different scales and a comparison of the runtime using a commercial solver. The results show that the modified Dijkstra algorithm has a runtime that is 100 times faster on average than the modified Floyd algorithm, which highlights its greater applicability in large-scale multimodal transportation networks, demonstrating that the proposed method both has practical significance and can generate satisfactory solutions to the multi-objective shortest path problem with multimodal transportation in the context of emergency logistics.
Cited by 8Open access
Hayi Mohamed Yassine, Chouiref Zahira · 2020
The problem of finding the shortest path is a combinatorial well-studied optimization problem, this last decade and is a challenging task over large graphs. This article presents an improved optimization Genetic algorithm (IOGA) to solve the k shortest paths problem. Our algorithm based on the combination of the exact algorithm (Dijkstra) and metaheuristic algorithm (Genetic algorithm-GA) is proposed to return the k shortest optimal paths on graph in large-scale routing problems. Our empirical results show that the proposed algorithm surpasses and runs faster than Dijkstra's algorithm and gives one or more paths,, while Dijkstra gives only one path.
Cited by 8
Alija, Amani Saleh · UTHM Institutional Repository (Universiti Tun Hussein Onn Malaysia) · 2015
There are so many algorithms used to find the shortest path such as Dijkstra, A* algorithm, Genetic algorithm, Floyd algorithm and Ant algorithm. In this study, two algorithms will be focused on. This study compares the Dijkstra’s, and A* algorithm to estimate search time and distance of algorithms to find the shortest path. It needs the appropriate algorithm to search the shortest path. Therefore, the purpose of this research is to explore which is the best shortest path algorithm by comparing the two types of algorithms. Such that it can be used to solve the problem path, search to analyze their efficiency in an environment based on two dimensional matrix which is best because of lookup time. This study implements the algorithm in visual C++ 2008 and design interface for the algorithms that allow the user to find the shortest path with the search time and the distance by determine the size of map, starting node and the destination node. The experimental result showed the search time of A* algorithm is faster than Dijkstra’s algorithm with average value 466ms and the distance is same of the both of algorithms.
Cited by 7Open access
Weiyi Zhu, Shinan Zhu, Xueqin Zhang et al. · 2019
Path planning of lunar robots is the guarantee that lunar robots can complete tasks safely and accurately. Aiming at the shortest path and the least energy consumption, an adaptive potential field ant colony algorithm (A-APFACO) suitable for path planning of lunar robot was proposed to solve the problems of slow convergence speed and easy to fall into local optimum of ant colony algorithm. This algorithm combines the artificial potential field method with ant colony algorithm, introduces the inducement heuristic factor, and adjusts the state transition rule of the ant colony algorithm dynamically, so that the algorithm has higher global search ability and faster convergence speed. The simulation experiment results show that the convergence speed of the improved adaptive ant colony algorithm is significantly faster, and the success rate of global searching for the shortest path can reach 96%.
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Hiroki Yanagisawa, Hiroki Yanagisawa · 2006
For solving the multicommodity flow problems, Lagrangian relaxation based algorithms are fast in practice. The time-consuming part of the algorithms is the shortest path computations in solving the Lagrangian dual problem. We show that an A * search based algorithm is faster than Dijkstra’s algorithm for the shortest path computations when the number of demands is relatively smaller than the size of the network.
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Tianyu Liu, CUICUI LUO · 2024
The shortest path problem has always been the most fundamental but extremely important problem in operations research and optimization research. Given a weighted graph (directed or undirected) 𝐺 = (𝑉, 𝐸, 𝜔) , |𝑉| = 𝑛, |𝐸| = 𝑚, and the two points s and t in G are the starting and ending points, respectively. The single source and single endpoint shortest path problem aims to find the shortest s-t path. The main contributions of this article are as follows: (1) Based on the cycle-reducing algorithm, algorithm, a hierarchical single-source single-sink shortest path algorithm is obtained. The advantage of this algorithm is that it runs faster and avoids accessing all vertices in the graph to save time and storage space. (2) Based on the 𝐴∗ algorithm, a new lower bound distance estimation function is proposed to solve the single source and single endpoint problem. (3) Propose a dynamic simulation-based method for solving the shortest path problem: embed a nonnegative weighted graph into Euclidean space and use dynamic simulation software to solve the shortest s-t path. The advantage of this method is that it is very accurate and can solve all the shortest s-t paths without visiting too many keyless points.
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Liam Roditty, Uri Zwick · ACM Transactions on Algorithms · 2012
Let G = ( V,E ) be a directed graph and let P be a shortest path from s to t in G . In the replacement paths problem, we are required to find, for every edge e on P , a shortest path from s to t in G that avoids e . The only known algorithm for solving the problem, even for unweighted directed graphs, is the trivial algorithm in which each edge on the path, in its turn, is excluded from the graph and a shortest paths tree is computed from s . The running time is O ( mn + n 2 log n ). The replacement paths problem is strongly motivated by two different applications: (1) The fastest algorithm to compute the k simple shortest paths between s and t in directed graphs [Yen 1971; Lawler 1972] computes the replacement paths between s and t . Its running time is Õ ( mnk ). (2) The replacement paths problem is used to compute the Vickrey pricing of edges in a distributed network. It was raised as an open problem by Nisan and Ronen [2001] whether it is possible to compute the Vickrey pricing faster than n computations of a shortest paths tree. In this article we present the first nontrivial algorithm for computing replacement paths in unweighted directed graphs (and in graphs with small integer weights). Our algorithm is Monte-Carlo and its running time is Õ ( m √ n ). This result immediately improves the running time of the two applications mentioned above in a factor of √ n . We also show how to reduce the problem of computing k simple shortest paths between s and t to O ( k ) computations of a second simple shortest path from s to t each time in a different subgraph of G . The importance of this result is that computing a second simple shortest path may turn out to be an easier problem than computing the replacement paths, thus, we can focus our efforts to improve the k simple shortest paths algorithm in obtaining a faster algorithm for the second shortest path problem.
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Gerald G. Brown, W. Matthew Carlyle · INFORMS journal on computing · 2019
We introduce a simple modification to the repeated shortest-path algorithm for the all-pairs shortest-path problem that adds a cumulative distance label update at each iteration based on the shortest-path tree from the prior iteration. We have implemented and tested our update using several shortest-path algorithms on a range of test networks of varying size, degree, and “skewness” (i.e., asymmetry) of costs on antisymmetric arcs, and we find that it provides a significant speedup to any such algorithm, except for cases either in which the underlying graph is extremely sparsely connected (or even disconnected) or when the arc costs are highly nonsymmetric. An added charm is that our best-modified method preserves the polynomial worst case runtime of its label-correcting antecedent. As with other repeated shortest-path algorithms, it is significantly faster than the Floyd–Warshall algorithm on sparsely connected networks and even some fairly densely connected networks.
Cited by 2
John A. Pavlik, Edward C. Sewell, Sheldon H. Jacobson · INFORMS journal on computing · 2021
This paper presents a new bidirectional search algorithm to solve the shortest path problem. The new algorithm uses an iterative deepening technique with a consistent heuristic to improve lower bounds on path costs. The new algorithm contains a novel technique of filtering nodes to significantly reduce the memory requirements. Computational experiments on the pancake problem, sliding tile problem, and Rubik’s cube show that the new algorithm uses significantly less memory and executes faster than A* and other state-of-the-art bidirectional algorithms. Summary of Contribution: Quickly solving single-source shortest path problems on graphs is important for pathfinding applications and is a core problem in both artificial intelligence and operations research. This paper attempts to solve large problems that do not easily fit into the available memory of a desktop computer, such as finding the optimal shortest set of moves to solve a Rubik’s cube, and solve them faster than existing algorithms.
Cited by 1