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Improved Yen's Algorithm for 2nd-Shortest Path Problem

Jie Tian · SSRN Electronic Journal · 2025

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Application of the Yen's algorithm to the continuous single refueling station location problem on a circuit network

Sang Jin Kweon · 2018

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k-shortest path: average-case analysis and practical improvements

Alexander Schickedanz · 2023

The single-source shortest-path problem is a fundamental problem in computer science. We consider a generalization of the shortest-path problem, the $k$-shortest path problem. Let $G$ be a directed edge-weighted graph with $n$ nodes and $m$ edges and $s,t$ be two fixed nodes. The goal is to compute $k$ paths $P_1,\dots,P_k$ between two fixed nodes $s$ and $t$ in non-decreasing order of their length such that all other paths between $s$ and $t$ are at least as long as the $k$\nth path $P_k$. We focus on the version of the $k$-shortest path problem where the paths are not allowed to visit nodes multiple times, sometime referred to as $k$-shortest simple path problem. The probably best known $k$-shortest path algorithm is Yen's algorithm. It has a worst-case time complexity of O(kn\cdot scp(n,m)), where scp(n,m) is the complexity of the single-source shortest-path algorithm used as a subroutine. In case of Dijkstra's algorithm scp(n,m) is O(m + n\log n). One of the more recent improvements of Yen's algorithm is by Feng. Even though Feng's algorithm is much faster in practice, it has the same worst-case complexity as Yen's algorithm. The main results presented in this thesis are upper bounds on the average-case of Yen's and Feng's algorithm, as well as practical improvements and a parallel implementation of Yen's and Feng's algorithms including these improvements. The implementation is publicly available under GPLv3 open source license. We show in our analysis that Yen's algorithm has an average-case complexity of O(k \log(n)\cdot scp(n,m)) on G(n,p) graphs with at least logarithmic average-degree and random edge weights following a distribution with certain properties. On G(n,p) graphs with constant to logarithmic average-degree and uniform random edge-weights over $[0;1]$, we show an average-case complexity of O(k\cdot\frac{\log^2 n}{np}\cdot scp(n,m)). Feng's algorithm has an even better average-case complexity of O(k\cdot scp(n,m)) on unweighted G(n,p) graphs with logarithmic average-degree and for constant values of $k$. We further provide evidence that the same holds true for G(n,p) graphs with uniform random edge-weights over $[0;1]$. On the practical side, we suggest new heuristics to prune even more single-source shortest-path computations than Feng's algorithm and evaluate all presented algorithms on G(n,p) and Grid graphs with up to 256 million nodes. We demonstrate speedups by a factor of up to 40 compared to Feng's algorithm. Finally we discuss two ways to parallelize the suggested algorithms and evaluate them on grid graphs showing speedups by a factor of 2 using 4 threads and by a factor of up to 8 using 16 threads, respectively.

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Traffic-Aware Navigation in Road Networks

Sarah Nassar · arXiv (Cornell University) · 2026

This project compares three graph search approaches for the task of traffic-aware navigation in Kingston's road network. These approaches include a single-run multi-query preprocessing algorithm (Floyd-Warshall-Ingerman), continuous single-query real-time search (Dijkstra's and A*), and an algorithm combining both approaches to balance between their trade-offs by first finding the top K shortest paths then iterating over them in real time (Yen's). Dijkstra's and A* resulted in the most traffic-aware optimal solutions with minimal preprocessing required. Floyd-Warshall-Ingerman was the fastest in real time but provided distance based paths with no traffic awareness. Yen's algorithm required significant preprocessing but balanced between the other two approaches in terms of runtime speed and optimality. Each approach presents advantages and disadvantages that need to be weighed depending on the circumstances of specific deployment contexts to select the best custom solution. *This project was completed as part of ELEC 844 (Search and Planning Algorithms for Robotics) in the Fall 2025 term.

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Traffic-Aware Navigation in Road Networks

Nassar, Sarah · arXiv (Cornell University) · 2026

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GNN-Aided Efficient Multipath Routing in Satellite Constellation Networks

Guoxing Yu, Mi Kyung Kwak, Siwoong Park et al. · 2025

This paper proposes a graph neural network (GNN) based framework to predict dynamic Inter Satellite Link (ISL) topology under Free Space Optical Communication (FSOC) constraints. The GNN model captures both local connectivity and global structural patterns in the satellite graph. The output of the GNN is used to construct a predicted adjacency matrix, over which routing paths are computed using Yen's k-shortest path algorithm.

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Parallel algorithms for digital map path optimisation

Hislop, Andrew David · ePrints Soton (University of Southampton) · 1992

<p>Working out the best route for a land vehicle to take from its current position to a certain destination can be done relatively quickly and easily by a human, given a map of the area. However, if the map is large and complex, and there are many different constraints on the route taken, then it should be faster to find the optimal route using a computer. Moreover, if the process can be distributed to run on several computers in parallel, the results will be obtained even more quickly. This thesis describes an investigation into finding fast and efficient implementations of parallel algorithms to solve the problem, given a digital map of the area. The target architecture is of the distributed memory MIMD variety and for the particular implementation described in this thesis, a transputer array was used. Firstly, a study of sequential optimum path-finding algorithms is given. Out of the four main algorithms: dynamic programming, Dijkstra's algorithm, d'Esopo's algorithm and branch-and-bound, d'Esopo's algorithm is verified by experiment to be the fastest. The results of distributing Yen's algorithm, a version of dynamic programming, and of distributing d'Esopo's algorithm, are then given. Parallel Yen is found to be fast and have an almost linear improvement in performance with the number of transputers used. However, its performance deteriorates rapidly as the map size is increased. Three different parallel versions of d'Esopo's algorithm are described. Although each is found to have high communication overheads, and to be slower than parallel Yen for the relatively small map sizes used, it is shown that the performances of the second and third parallel d'Esopo programs improve relative to Yen's as the map size is increased. Finally, it is shown how one of these parallel d'Esopo algorithms would be suitable for implementing in a distributed architecture vehicle guidance system.</p>

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A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph

Denis Kurz, Petra Mutzel · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2016

We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein’s algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm [Networks, 1971] and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n+m) additional time per path in well-behaved cases, where n is the number of nodes and m is the number of edges. Our computational results show that on random graphs and large road networks, these well-behaved cases are quite common and our algorithm is faster than existing algorithms by an order of magnitude.

Cited by 3Open access

K-best enumeration - theory and application

Kurz, Denis · Eldorado - Repository of the TU Dortmund (TU Dortmund University) · 2017

Where an optimal solution does not contain sufficient information about a given problem instance, enumerating good solutions is a common coping strategy. In combinatorial optimization, k-best enumeration, or ranking, has been studied and applied extensively. The k shortest simple path problem in directed, weighted graphs (kSSP), introduced in 1963 by Clarke, Krikorian and Rausen, is particularly well known. Efficient existing algorithms are based on Yen's algorithm for this problem; they all feature a worst-case running time of O(kn(m + n log n)) on a graph with n vertices and m edges. Vassilevska Williams and Williams show that a polynomially faster kSSP algorithm would also result in an algorithm for the all-pairs shortest path problem with running time O(n\^{3-ε}), which seems unlikely at the moment. We present a kSSP algorithm that is not based on Yen's algorithm, matching the state-of-the-art running time of O(kn(m + n log n)). In particular, we do not solve a single instance of the replacement path problem, a basic building block of Yen's algorithm. Instead, we make use of ideas used in Eppstein's algorithm for a similar problem where paths are allowed to be non-simple. Using our algorithm, one may find Θ(m) simple paths with a single shortest path tree computation and additional O(m + n) time per path in well-behaved cases. We also propose practical improvements for our algorithm, comprising dynamic edge pruning, lazy shortest path tree computations, and fast path simplicity checks. In a detailed computational study, we demonstrate that well-behaved cases are quite common in random graphs, grids and road networks. We showcase usefulness of the dynamic edge pruning approach on those three graph classes and on network topology graphs. Despite 40 years of heavy research on Yen-based kSSP algorithms, including involved algorithm engineering, our algorithm proves to be faster than existing algorithms by at least an order of magnitude. However, there is not much room for improvement for the general worst case. We demonstrate that kSSP can be solved considerably faster if the input graph is restricted to have bounded treewidth. Specifically, we propose an algorithm template for enumerating the k best solutions in a bounded treewidth graph for any problem that can be expressed in counting monadic second-order logic. Our template is a generalization of Courcelle's theorem, mainly utilizing dynamic programming and a persistent heap data structure. It enumerates any constant amount of solutions in time O(n). For general k, it requires O(log n) extra time per solution, resulting in a total running time of O(n + k log n). Finding the initial solution is parallelizable, so the linear term can be dropped and we obtain a running time of O(k log n) in the PRAM model. The class of problems expressible in counting monadic second order logic contains kSSP, matching problems, or the spanning tree problem, but also a number of NP-hard problems like the traveling salesman problem, where we achieve a doubly-exponential speedup.

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A Comparison of Shortest Path Algorithms Applied to Sparse Graphs

B.L. Hulme, Bernie Hulme, USNRC et al. · 1978

Three methods are compared for finding shortest paths from one node to all other nodes in sparse, nonnegatively weighted, directed graphs. Dijkstra's method with a heap sort, Ford's method with a sequence list, and Yen's method are considered the best representatives of certain classes of methods for this problem. They have essentially the same storage requirements and are compared on the basis of algorithm execution time for a test set of randomly generated problems. For directed graphs that are sufficiently sparse, Ford's method with a sequence list is the fastest of the three methods. A different version of Ford's algorithm is proposed for use in the special case of undirected sparse graphs in order to make efficient use of the symmetry of the distance matrix.

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Block-Based Methods for the Reconstruction of Finite-Length Signals From Nonuniform Samples

T. Engin Tuncer · IEEE Transactions on Signal Processing · 2007

Two novel block-based algorithms are presented for the reconstruction of uniform samples given the nonuniform samples. The first algorithm uses a sinc interpolator whereas the second one uses a DFT-based interpolator. It is shown that the proposed algorithms are stable and the error due to noise and sampling jitter is bounded by the corresponding error norms of noise and jitter, respectively. We show that both of the block-based algorithms provide nearly perfect reconstruction for a class of practically time and bandlimited signals. Boundary effects are considered and single and multiblock processing is discussed. A modified block-based algorithm is developed by using the windowing technique in order to improve the mean-squared error (MSE) performance for nonbandlimited signals. It is shown that this algorithm performs better than a group of alternative algorithms, including Yen's third algorithm, for a variety of signal, noise, and sampling grids

Cited by 23Open access

Adaptive modulation allocation algorithm in elastic optical networks

Sabi Y.M. Bandiri, Tales Cleber Pimenta, Fábio Renan Durand et al. · International Journal of Communication Systems · 2020

Summary This paper introduces a new way to allocate the modulation format and improves the energy efficiency in elastic optical networks. For every connection request, both the quality of transmission and quality of service requirements are investigated. The allocation of modulation formats is based on both the physical distance and the required number of frequency slots. To improve the energy efficiency, Yen's algorithm is executed for every connection requested, and the lightpath with the lowest power consumption is selected. Numerical results were compared with adaptive modulation algorithms presented in the existing literature. The energy efficiency was improved by up to 27%, the used bandwidth available was reduced by up to 60%, and the blocking probability was decreased by 30% using our proposed adaptive algorithm.

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Efficient Multipath Routing Scheme for MPTCP-enable Software-Defined Networks

Nguyễn Anh Tuấn, Linh Nguyen, Tien Vu Huu et al. · 2021

In this paper, we study the multipath routing problem in MPTCP-enable software-defined networks. We have proposed an efficient multipath routing algorithm for creating bandwidth-abundant and flexible future software-defined core networks. Our proposed algorithm will figure out k-least-jointed shortest paths by using conventional k-shortest path algorithm, e.g., Yen's algorithm, incorporating with a greedy algorithm for the path selection. Thanks to that, the algorithm can help to exploit the use of MPTCP while reducing the bottleneck problem that may occur with shared links in the networks. In order to verify the efficiency of our proposal, we have implemented an MPTCP-enable software-defined testbed based on mininet, Ryu controller, and Kali Linux OS and perform numerical experiments to compare the network performance of our approach to traditional MPTCP as well as conventional TCP (without MPTCP). The obtained results confirmed that, by reducing the number of jointed links in the set of selected k-shortest paths, our solution outperforms the traditional MPTCP as well as that of conventional TCP networks.

Cited by 2

Signal reconstruction from nonuniform samples

Serdaroğlu, Bülent · OpenMETU (Middle East Technical University) · 2019

Sampling and reconstruction is used as a fundamental signal processing operation since the history of signal theory. Classically uniform sampling is treated so that the resulting mathematics is simple. However there are various instances that nonuniform sampling and reconstruction of signals from their nonuniform samples are required. There exist two broad classes of reconstruction methods. They are the reconstruction according to a deterministic, and according to a stochastic model. In this thesis, the most fundamental aspects of nonuniform sampling and reconstruction, according to a deterministic model, is analyzed, implemented and tested by considering specific nonuniform reconstruction algorithms. Accuracy of reconstruction, computational efficiency and noise stability are the three criteria that nonuniform reconstruction algorithms are tested for. Specifically, four classical closed form interpolation algorithms proposed by Yen are discussed and implemented. These algorithms are tested, according to the proposed criteria, in a variety of conditions in order to identify their performances for reconstruction quality and robustness to noise and signal conditions. Furthermore, a filter bank approach is discussed for the interpolation from nonuniform samples in a computationally efficient manner. This approach is implemented and the efficiency as well as resulting filter characteristics is observed. In addition to Yen's classical algorithms, a trade off algorithm, which claims to find an optimal balance between reconstruction accuracy and noise stability is analyzed and simulated for comparison between all discussed interpolators. At the end of the stability tests, Yen's third algorithm, known as the classical recurrent nonuniform sampling, is found to be superior over the remaining interpolators, from both an accuracy and stability point of view.

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Düzgün olmayan örneklerinden sinyal yapılandırması.

Serdaroğlu, Bülent · OpenMETU (Middle East Technical University) · 2005

Sampling and reconstruction is used as a fundamental signal processing operation since the history of signal theory. Classically uniform sampling is treated so that the resulting mathematics is simple. However there are various instances that nonuniform sampling and reconstruction of signals from their nonuniform samples are required. There exist two broad classes of reconstruction methods. They are the reconstruction according to a deterministic, and according to a stochastic model. In this thesis, the most fundamental aspects of nonuniform sampling and reconstruction, according to a deterministic model, is analyzed, implemented and tested by considering specific nonuniform reconstruction algorithms. Accuracy of reconstruction, computational efficiency and noise stability are the three criteria that nonuniform reconstruction algorithms are tested for. Specifically, four classical closed form interpolation algorithms proposed by Yen are discussed and implemented. These algorithms are tested, according to the proposed criteria, in a variety of conditions in order to identify their performances for reconstruction quality and robustness to noise and signal conditions. Furthermore, a filter bank approach is discussed for the interpolation from nonuniform samples in a computationally efficient manner. This approach is implemented and the efficiency as well as resulting filter characteristics is observed. In addition to Yen's classical algorithms, a trade off algorithm, which claims to find an optimal balance between reconstruction accuracy and noise stability is analyzed and simulated for comparison between all discussed interpolators. At the end of the stability tests, Yen's third algorithm, known as the classical recurrent nonuniform sampling, is found to be superior over the remaining interpolators, from both an accuracy and stability point of view.

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A Fast Randomized Method to Find Homotopy Classes for Socially-Aware Navigation

Luigi Palmieri, Andrey Rudenko, Kai Oliver Arras · arXiv (Cornell University) · 2015

We introduce and show preliminary results of a fast randomized method that finds a set of K paths lying in distinct homotopy classes. We frame the path planning task as a graph search problem, where the navigation graph is based on a Voronoi diagram. The search is biased by a cost function derived from the social force model that is used to generate and select the paths. We compare our method to Yen's algorithm, and empirically show that our approach is faster to find a subset of homotopy classes. Furthermore our approach computes a set of more diverse paths with respect to the baseline while obtaining a negligible loss in path quality.

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Regulation, Quality Adjustment, and Relative Price Changes: The Case of the Yen Appreciation Shock of 1985

Kaku Furuya · Palgrave Macmillan UK eBooks · 2012

One of the best-known events in the post-war economic history of Japan is the sharp appreciation of the yen in the mid-1980s. The dollar– yen exchange rate, which had been hovering around ¥240/$ during the early 1980s (between the inauguration of the Reagan Administration in January 1981 and the Plaza Agreement in September 1985), tumbled to ¥122/$ in December 1987, almost doubling the yen's value in two years. (See Figure13.1.) Both the magnitude and speed of appreciation were unprecedented, whose record has not been broken until now.1 KeywordsExchange RateIndifference CurveEmpirical IssueIndirect Utility FunctionTradable PriceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Pathly: The integrated system for finding diverse journey methods

Prachya Boonsri, Thanakon Kaewkanha, Jaturon Namwiset et al. · 2016

Public Transportation is a crucial factor for a journey not only the traveler but also people who live in Bangkok. From the variety of routes and many types of transport services that make a trip to Bangkok from one place to another would probably be shown by different ways. Pathly is our proposed algorithm which aims to develop the mobile applications that can suggest the diverse methods for a journey by the public transportation in Bangkok. It can make the appropriate choices considering from each condition and achieve user satisfaction. In our proposed, we implement the K-shortest path algorithm which is Yen's algorithm for finding the diversity of routes. We design and collect all data from the graph database. We kept all data as a graph structure which represents the station as vertex and represents the path between 2 adjacent stations as an edge. Moreover, we make our consideration of 2 significant factors of a journey as time, fare over the trip. Pathly will help users to find the multiple methods to go to anywhere in Bangkok with an appropriate choice.

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Evaluating the 2PC Algorithm for the Maintenance of P2P Live Streaming

Adriel Cardoso dos Santos, Iago A. Carvalho, Cristiano M. Silva et al. · IEEE Latin America Transactions · 2024

Peer-to-Peer (P2P) Networks for live streaming face challenges such as ensuring low latency and low discontinuity in media transmission among peers. Algorithms for constructing and maintaining the overlay are often proposed to address several of these challenges. However, it is common to find works that present positive results from the execution of these algorithms without showing the overlay structure constructed by them. In this article, we analyze the overlay constructed and maintained by the Peer Classification for Partnership Constraints (2PC) algorithm. 2PC proved to be efficient in dealing with a large number of free-riders on the network, imposing constraints on partnerships between peers according to their contributions to media transmission. To understand the 2PC execution effects supported by the K-Shortest Path Yen's algorithm, we evaluated the application of the 2PC and identified that the partnership relationships between peers imposed by the algorithm organize the overlay attracting high-contribution peers close to the server, while pushing low-contribution peers to the edge of the overlay.

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Backup Resource Allocation Model with Probabilistic Protection Considering Service Delay

Shinya Horimoto, Fujun He, Eiji Oki · IEICE Transactions on Communications · 2023

This paper proposes a backup resource allocation model for virtual network functions (VNFs) to minimize the total allocated computing capacity for backup with considering the service delay. If failures occur to primary hosts, the VNFs in failed hosts are recovered by backup hosts whose allocation is pre-determined. We introduce probabilistic protection, where the probability that the protection by a backup host fails is limited within a given value; it allows backup resource sharing to reduce the total allocated computing capacity. The previous work does not consider the service delay constraint in the backup resource allocation problem. The proposed model considers that the probability that the service delay, which consists of networking delay between hosts and processing delay in each VNF, exceeds its threshold is constrained within a given value. We introduce a basic algorithm to solve our formulated delay-constraint optimization problem. In a problem with the size that cannot be solved within an acceptable computation time limit by the basic algorithm, we develop a simulated annealing algorithm incorporating Yen's algorithm to handle the delay constraint heuristically. We observe that both algorithms in the proposed model reduce the total allocated computing capacity by up to 56.3% compared to a baseline; the simulated annealing algorithm can get feasible solutions in problems where the basic algorithm cannot.

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