• 한국경영과학회지
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• 제26권3호
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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.

• 한국국방경영분석학회지
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• 제17권2호
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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.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2002년도 춘계공동학술대회
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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 $K{\leq}3$.

• 경영과학
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• 제15권2호
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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.

• 경영과학
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• 제25권2호
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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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• 제17권1_2_3호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2006년도 추계학술대회
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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.

• 대한교통학회지
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• 제23권8호
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• pp.113-128
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• 2005

일반적으로 현실(특히 도시) 교통망에서 교차로를 반복해서 방문하는 통행은 존재하지만, 가로를 반복해서 주행하는 현상은 존재하지 않는다. 교통망에서의 루프형 통행은 링크의 반복이 허용되지 않는 링크 비루프(Link Loopless Path) 통행으로 축소된다. 본 연구에서는 K개의 경로탐색에서 기존의 방식과 달리 Heap Ordered Tree를 이용하여 월등한 수행속도(최악의 경우) O(m+ n log n+ K log K)로서 수행되는 Eppstein 알고리즘과 Jimenez et al의 LVEA을 고찰하여, 이들 알고리즘의 문제점인 링크루프의 발생을 제어하는 방안을 제어하도록 한다. 사례연구를 통하여 제안된 알고리즘을 검증 평가한다.

• 한국국방경영분석학회지
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• 제16권2호
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• pp.105-117
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• 1990

In the transportation network problems, it is often more desirable to select multiple number of optimal parths to prepare for additional constratints being imposed than to choose single optimal path. This paper addresses 'the problem of finding the k-shortest paths visiting p-specified nodes in a network'. The solution method is derived and the example of application is shown. The keypoint for determining the k-shortest paths via p-specified nodes is to combine the Shier's k-shortest path algorithm and the principle of optimality of dynamic programming method. Finally, for a transportation network problem consisting of national main routes, the k-shortest paths via some specified cites are obtained by using the solution method developed here.

• 한국국방경영분석학회지
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• 제25권1호
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• pp.29-36
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• 1999

In this paper, we are concerned with the K-shortest loopless path problem. The MPS algorithm, recently proposed by Martins et al., finds paths efficiently because it solves the shortest path problem only one time unlike other algorithms. But its computational complexity has not been known yet. We propose a few techniques by which the MPS algorithm can be implemented efficiently. First, we use min-heap data structure for the storage of candidate paths in order to reduce searching time for finding minimum distance path. Second, we prevent the eliminated paths from reentering in the list of candidate paths by lower bounding technique. Finally, we choose the source mode as a deviation node, by which selection time for the deviation node is reduced and the performance is improved in spite of the increase of the total number of candidate paths.