• Korean Management Science Review
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• v.15 no.2
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• pp.229-237
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• 1998

This paper presents a new algorithm for the K Shortest Paths Problem which is developed with a Double Shortest Arborescence and an inward arc breaking method. A Double Shortest Arborescence is made from merging a forward shortest arborescence and a backward one with Dijkstra algorithm. and shows us information about each shorter path to traverse each arc. Then K shorter paths are selected in ascending order of the length of each short path to traverse each arc, and some paths of the K shorter paths need to be replaced with some hidden shorter paths in order to get the optimal paths. And if the cross nodes which have more than 2 inward arcs are found at least three times in K shorter path, the first inward arc of the shorter than the Kth shorter path, the exposed path replaces the Kth shorter path. This procedure is repeated until cross nodes are not found in K shorter paths, and then the K shortest paths problem is solved exactly. This algorithm are computed with complexity o($n^3$) and especially O($n^2$) in the case K=3.

• 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.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.12 no.6
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• pp.1-9
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• 2013

The studies on the shortest path algorithms based on Dijkstra algorithm has been done continuously to decrease the time for searching. $A^*$ algorithm is the most represented one. Although fast searching speed is the major point of $A^*$ algorithm, there are high rates of failing in search of the shortest path, because of complex and irregular networks. The failure of the search means that it either did not find the target node, or found the shortest path, witch is not true. This study proposed $A^*$ algorithm applying method that can reduce searching failure rates, preferentially organizing the relations between the starting node and the targeting node, and appling it in reverse according to the organized path. This proposed method may not build exactly the shortest path, but the entire failure in search of th path would not occur. Following the developed algorithm tested in a real complex networks, it revealed that this algorithm increases the amount of time than the usual $A^*$ algorithm, but the accuracy rates of the shortest paths built is very high.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.11
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• pp.634-639
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• 2002

A Shortest Path Algorithm is the method to find the most efficient route among many routes from a start node to an end node. It is based on Labeling methods. In Labeling methods, there are Label-Setting method and Label-Correcting method. Label-Setting method is known as the fastest one among One-to-One shortest path algorithms. But Benjamin[1,2] shows Label-Correcting method is faster than Label-Setting method by the experiments using large road data. Since Graph Growth algorithm which is based on Label-Correcting method is made to find One-to-All shortest path, it is not suitable to find One-to-One shortest path. In this paper, we propose a new One-to-One shortest path algorithm. We show that our algorithm is faster than Graph Growth algorithm by extensive experiments.

• Korean Management Science Review
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• v.19 no.1
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• pp.55-66
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• 2002

Given a directed network, a designated arc, and lowers and upper bounds for the distance of each arc, the preprocessing shortest path problem Is a decision problem that decides whether there is some choice of distance vector such that the distance of each arc honors the given lower and upper bound restriction, and such that the designated arc is on some shortest path from a source node to a destination notre with respect to the chosen distance vector. The preprocessing shortest path problem has many real world applications such as communication and transportation network management and the problem is known to be NP-complete. In this paper, we develop an algorithm that solves the problem using the structural properties of shortest paths.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.11B
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• pp.972-984
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• 2003

In this paper, new on-line routing algorithms with a bandwidth constraint are proposed. The proposed algorithms may be used for a dynamic LSP setup in MPLS network. We extend the WSP algorithm, the SWP algorithm and a utilization-based routing algorithm into the proposed algorithms by slightly modified K-shortest loopless path algorithms. The performances such as accepted bandwidth, accepted request number and average path length of the proposed and the previous algorithms are evaluated through extensive simulations. All simulations are conducted under the condition that any node can be an ingress or egress node for a LSP setup. The simulation results show that the proposed algorithms have the good performances in most cases in comparison to the previous algorithms. Under the heavy load condition, the algorithms based on the minimum hop path perform better than any other algorithms.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.893-900
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• 2007

This paper suggests an algorithm that improves the disadvantages of the Dijkstra algorithm that is commonly used in GPS navigation system, searching for the shortest path. Dijkstra algorithm, first of all, requires much memory for the performance of the algorithm. It has to carry out number of node minus 1, since it determines the shortest path from all the nodes in the graph, starting from the first node. Therefore, Dijkstra algorithm might not be able to provide the information on every second, searching for the shortest path between the roads of the congested city and the destination. In order to solve these problems, this paper chooses a method of searching a number of nodes at once by means of choosing the shortest path of all the path nodes (select of minimum weight arc in-degree and out-degree), excluding the departure and destination nodes, and of choosing all the arcs that coincide with the shortest path of the path nodes, from all the node outgoing arcs starting from the departure node. On applying the suggested algorithm to 14 various digraphs, we succeeded to search the shortest path. In addition, the result was obtained at the speed of 2 to 3 times faster than that of Dijkstra algorithm, and the memory required was less than that of Dijkstra algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.8-14
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• 2002

This article presents a new algorithm for the K Shortest Paths Problem which develops initial K shortest paths, and repeal to expose hidden shortest paths with dual approach and to replace the longest path in the present K paths. The initial solution which comprises K shortest paths among shortest paths to traverse each arc 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, one inward arc of this crossing node, which has minimum detouring distance, is chosen, and a new 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. This algorithm, requires worst case time complexity of $O(Kn^2),\;and\;O(n^2)$ in the case $K{\leq}3$.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.8
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• pp.74-84
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• 2010

In this paper, we propose a preference-based shortest path algorithm which is combined with Ant Colony Optimization (ACO) and A* heuristic algorithm. In recent years, with the development of ITS (Intelligent Transportation Systems), there has been a resurgence of interest in a shortest path search algorithm for use in car navigation systems. Most of the shortest path search algorithms such as Dijkstra and A* aim at finding the distance or time shortest paths. However, the shortest path is not always an optimum path for the drivers who prefer choosing a less short, but more reliable or flexible path. For this reason, we propose a preference-based shortest path search algorithm which uses the properties of the links of the map. The preferences of the links are specified by the user of the car navigation system. The proposed algorithm was implemented in C and experiments were performed upon the map that includes 64 nodes with 118 links. The experimental results show that the proposed algorithm is suitable to find preference-based shortest paths as well as distance shortest paths.

• Journal of the military operations research society of Korea
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• v.18 no.2
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• pp.66-95
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• 1992

Shortest paths are one of the simplest and most widely used concepts in deterministic networks. A decison of troops movement route can be analyzed in the network with a shortest path algorithm. But in reality, the value of arcs can not be determined in the network by crisp numbers due to imprecision or fuzziness in parameters. To account for this reason, a fuzzy network should be considered. A fuzzy shortest path can be modeled by general fuzzy mathematical programming and solved by fuzzy dynamic programming. It can be formulated by the fuzzy network with lingustic variables and solved by the Klein algorithm. This paper focuses on a revised fuzzy shortest path algorithm and an application is discussed.