• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.3
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• pp.79-94
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• 2001

This paper presents a new algorithm for the K shortest paths Problem which develops initial K shortest paths, and repeat to expose hidden shortest paths with dual approach and to replace the longest path in the present K paths. The initial solution comprises K shortest paths among shortest paths to traverse each arc in a Double Shortest Arborescence which is made from bidirectional Dijkstra algorithm. When a crossing node that have two or more inward arcs is found at least three time by turns in this K shortest paths, there may be some hidden paths which are shorter than present k-th path. To expose a hidden shortest path, one inward arc of this crossing node is chose by means of minimum detouring distance calculated with dual variables, and then the hidden shortest path is exposed with joining a detouring subpath from source to this inward arc and a spur of a feasible path from this crossing node to sink. If this exposed path is shorter than the k-th path, the exposed path replaces the k-th path. This algorithm requires worst case time complexity of O(Kn$^2$), and O(n$^2$) in the case k$\leq$3.

• Journal of the military operations research society of Korea
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• v.25 no.2
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• pp.73-83
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• 1999

In this paper, we consider the shortest path network problem with fixed charges. A turn penalty algorithm for the shortest path problem with fixed charges or turn penalties is presented, which is using the next node comparison method. The algorithm described here is designed to determine the shortest route in the shortest path network problem including turn penalties. Additionally, the way to simplify the computation for the shortest path problem with turn penalties was pursued.

• Journal of Korea Multimedia Society
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• v.20 no.4
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• pp.649-659
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• 2017

Typically, a smart car is equipped with access to the Internet and a wireless local area network. Moreover, a smart car is equipped with a global positioning system (GPS) based navigation system that presents a map to a user for recommending the shortest path to a desired destination. This paper presents the design and implementation of a real-time shortest path search system for directed and dynamic roads. Herein, we attempt to simulate real-world road environments, while considering changes in the ratio of directed roads and in road conditions, such as traffic accidents and congestions. Further, we analyze the effect of the ratio of directed roads and road conditions on the communication cost between the server and vehicles and the arrival times of vehicles. In this study, we compare and analyze distance-based shortest path algorithms and driving time-based shortest path algorithms while varying the number of vehicles to search for the shortest path, road conditions, and ratio of directed roads.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.60-66
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• 2006

This paper presents a new algorithm for the K shortest path problem in a directed network. After a shortest path is produced with Dijkstra algorithm, detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set, this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated for the K-1 st path of the set. This algorithm can be applied to a problem of generating the detouring paths in the navigation system for ITS and also for vehicle routing problems.

• Journal of the military operations research society of Korea
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• v.17 no.2
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• pp.72-89
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• 1991

In transportation network problems, it is often desirable to select multiple number of the shortect paths. On problems of finding these paths, algorithms have been developed to choose single shortest path, k-shortest paths and k-shortest paths via p-specified nodes in a network. These problems consider the time as the main factor. In wartime, we must consider availability as well as time to determine the shortest transportation path, since we must take into account enemy's threat. Therefore, this paper addresses the problem of finding the shortest transportation path considering both time and availability. To accomplish the objective of this study, values of k-shortest paths are computed using the algorithm for finding the k-shortest paths. Then availabilties of those paths are computed through simulation considering factors such as rates of suffering attack, damage and repair rates of the paths. An optimal path is selected using any one of the four decision rules that combine the value and availability of a path.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.5
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• pp.988-995
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• 2009

One of the most popular services of Telematics is a shortest path finding from a starting point to a destination. In this paper, a dynamic shortest path finding system with forecasting result of traffic flow in the future was developed and various experiments to verify the performance of our system using real-time traffic information has been conducted. Traffic forecasting has been done by a prediction system using Bayesian network. It searched a dynamic shortest path, a static shortest path and an accumulated shortest path for the same starting point and destination and calculated their travel time to compare with one of its real shortest path. From the experiment, over 75%, the travel time of dynamic shortest paths is the closest to one of their real shortest paths than one of static shortest paths and accumulated shortest paths. Therefore, it is proved that finding a dynamic shortest path by applying traffic flows in the future for intermediated intersections can give more accurate traffic information and improve the quality of services of Telematics than finding a static shortest path applying by traffic flows of the starting time for intermediated intersections.

• Journal of the military operations research society of Korea
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• v.26 no.2
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• pp.120-130
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• 2000

The purpose of this study is to present a method for determining the k most vital arcs in shortest path problem using an evolutionary algorithm. The problem of finding the k most vital arcs in shortest path problem is to find a set of k arcs whose simultaneous removal from the network causes the greatest increase in the total length of shortest path. Generally, the problem determining the k most vital arcs in shortest path problem has known as NP-hard. Therefore, in order to deal with the problem of real world the heuristic algorithm is needed. In this study we propose to the method of finding the k most vital arcs in shortest path problem using an evolutionary algorithm which known as the most efficient algorithm among heuristics. The method presented in this study is developed using the library of the evolutionary algorithm framework and then the performance of algorithm is analyzed through the computer experiment.

• Journal of Korean Society of Transportation
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• v.23 no.7 s.85
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• pp.149-158
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• 2005

The object of this paper is to develop the shortest path algorithm. The existing shortest path algorithm models are developed while considering travel time and travel distance. A few problems occur in these shortest path algorithm models, which have paid no regard to cognition of users, such as when user who doesn't have complete information about the trip meets a strange road or when the route searched from the shortest path algorithm model is not commonly used by users in real network. This paper develops a shortest path algorithm model to provide ideal route that many people actually prefer. In order to provide the ideal shortest path with the consideration of travel time, travel distance and road cognition, travel time is predicted by using Kalman filtering and travel distance is predicted by using GIS attributions. The road cognition is considered by using space data of GIS. Optimal routes provided from this paper are shortest distance path, shortest time path, shortest path considering distance and cognition and shortest path considering time and cognition.

• Korean Management Science Review
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• v.25 no.2
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• pp.81-88
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• 2008

This paper presents a new algorithm for the K shortest paths problem in a network. After a shortest path is produced with Dijkstra algorithm. detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set. this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated until the $K^{th}-1$ path of the set is obtained. The computational results for networks with about 1,000,000 nodes and 2,700,000 arcs show that this algorithm can be applied to a problem of generating the detouring paths in the metropolitan traffic networks.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.1-23
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• 2005

The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents an $O(n^2)$ time sequential algorithm and an $O(n^2/p+logn)$ time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, where p and n represent respectively the number of processors and the number of vertices of the circular-arc graph.