• 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.

• 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.

• 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.

• 대한교통학회지
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• 제22권4호
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• pp.85-96
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• 2004

합리적 통행경로는 "경로를 노드 또는 링크의 순서로 표현할 때, 경로를 구성하는 노드의 반복은 존재해도 링크의 반복은 존재하지 않는다"는 원리에 근거한다. 최적경로 탐색과정에서 합리적 통행현상을 포함하는 방법은 링크로 구성된 표지(Link-Based Label)를 적용하는 방안이 적용하기 용이하다. 링크표지를 활용하는 경우 링크의 중복 표현을 허용되지 않는 상황에서 노드의 중복표현이 가능하여 합리적인 통행을 원칙적으로 보장될 뿐만 아니라 목적지에서 출발지로 경로를 역 추적(Backward Trace)하는 과정에서 전 링크(Pvevious Link)의 단일정보만 이용하므로 Bellman의 최적원리(Optimality Condition)에 의한 최적해(Optimal Solution)가 보장된다. 본 연구는 다수의 경로를 선정함에 있어 합리적 통행행태를 고려하기 위한 링크표지고정방식(Link-Based Label Setting)을 제안한다. 기존에 표지고정(Label Setting)을 기반으로 제안되었던 노드기반 다수경로알고리즘을 기반으로 링크표지로 전환하는 방안을 개발한다. 또한 알고리즘의 대규모 교통망에 적용한 수행결과를 통해 대안경로정보제공을 위한 현실적용의 문제점을 도출하고, 도로의 연속주행을 보장하려는 운전자의 경로선택행태를 반영하는 방안에 대해 검토한다.

• Management Science and Financial Engineering
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• 제4권2호
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• pp.1-13
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• 1998

The Shortest Path Problem in Time-dependent Networks, where the travel time of each link depends on the time interval, is not realistic since the model and its solution violate the Non-passing Property (NPP:often referred to as FIFO) of real phenomena. Furthermore, solving the problem needs much more computational and memory complexity than the general shortest path problem. A new model for Time-dependent Networks where the flow speeds of each link depend on time interval, is suggested. The model is more realistic since its solution maintains the NPP. Solving the problem needs just a little more computational complexity, and the same memory complexity, as the general shortest path problem. A solution algorithm modified from Dijkstra's label setting algorithm is presented. We extend this model to the problem of Minimum Expected Time Path in Time-dependent Stochastic Networks where flow speeds of each link change statistically on each time interval. A solution method using the Kth-shortest Path algorithm is presented.