• 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.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.11-20
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• 1998

This paper deals with a mathematical model and an algorithm for the problem of determining k most vital arcs in the shortest path problem. First, we propose a 0-1 integer programming model for finding k most vital arcs in shortest path problem given the ordered set of paths with cardinality q. Next, we also propose an algorithm for finding k most vital arcs ln the shortest path problem which uses the 0-1 Integer programming model and shortest path algorithm and maximum flow algorithms repeatedly Malik et al. proposed a non-polynomial algorithm to solve the problem, but their algorithm was contradicted by Bar-Noy et al. with a counter example to the algorithm in 1995. But using our algorithm. the exact solution can be found differently from the algorithm of Malik et al.

• 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.

• 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 Korean Society for Precision Engineering
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• v.19 no.9
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• pp.142-150
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• 2002

This study describes a method of finding an optimal path of a soccer robot by using a concentric circle method with different radii of rotation. Comparing with conventional algorithms which try to find the shortest path length, the variable concentric circle method find the shortest moving time. The radius fur the shortest moving time for a given ball location depends on the relative location between a shooting robot and a ball. Practically it is difficult to find an analytical solution due to many unknowns. Assuming a radius of rotation within a possible range, total path moving time can be calculated by adding the times needed for straight path and circular path. Among these times the shortest time is obtained. In this paper, a graphical solution is presented such that the game ground is divided into 3 regions with a minimum, medium, and maximum radius of rotation.

• Journal of the Society of Naval Architects of Korea
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• v.50 no.5
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• pp.298-306
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• 2013

Nowadays, a transporter manager plans the schedule of the block transportation by considering the experience of the manager, the production process of the blocks and the priority of the block transportation in shipyard. The schedule planning of the block transportation should be rearranged for the reflection of the path blocking cases occurred by unexpected obstacles or delays in transportation. In this paper, the optimal block transportation path planning system is developed for rearranging the schedule of the block transportation by considering the damaged path. $A^*$ algorithm is applied to calculate the new shortest path between the departure and arrival of the blocks transported through the damaged path. In this algorithm, the first node of the damaged path is considered as the starting position of the new shortest path, and then the shortest path calculation is completed if the new shortest path is connected to the one of nodes in the original path. In addition, the data structure for the algorithm is designed. This optimal block transportation path planning system is applied to the Philippine Subic shipyard and the ability of the rapid path modification is verified.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.4 no.5
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• pp.939-955
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• 2010

With the progress of IT and mobile positioning technologies, various types of location-based services (LBS) have been proposed and implemented. Finding a shortest path between two nodes is one of the most fundamental tasks in many LBS related applications. So far, there have been many research efforts on the shortest path finding problem. For instance, $A^*$ algorithm estimates neighboring nodes using a heuristic function and selects minimum cost node as the closest one to the destination. Pruning method, which is known to outperform the A* algorithm, improves its routing performance by avoiding unnecessary exploration in the search space. For pruning, shortest paths for all node pairs in a map need to be pre-computed, from which a shortest path container is generated for each edge. The container for an edge consists of all the destination nodes whose shortest path passes through the edge and possibly some unnecessary nodes. These containers are used during routing to prune unnecessary node visits. However, this method shows poor performance as the number of unnecessary nodes included in the container increases. In this paper, we focus on this problem and propose a new border line-based pruning scheme for path routing which can reduce the number of unnecessary node visits significantly. Through extensive experiments on randomly-generated, various complexity of maps, we empirically find out optimal number of border lines for clipping containers and compare its performance with other methods.

• Journal of the Korea Society of Computer and Information
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• v.19 no.7
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• pp.103-111
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• 2014

This paper proposes a modified algorithm that improves on Dijkstra's algorithm by applying it to purely two-way traffic paths, given that a road where bi-directional traffic is made possible shall be considered as an undirected graph. Dijkstra's algorithm is the most generally utilized form of shortest-path search mechanism in GPS navigation system. However, it requires a large amount of memory for execution for it selects the shortest path by calculating distance between the starting node and every other node in a given directed graph. Dijkstra's algorithm, therefore, may occasionally fail to provide real-time information on the shortest path. To rectify the aforementioned shortcomings of Dijkstra's algorithm, the proposed algorithm creates conditions favorable to the undirected graph. It firstly selects the shortest path from all path vertices except for the starting and destination vertices. It later chooses all vertex-outgoing edges that coincide with the shortest path setting edges so as to simultaneously explore various vertices. When tested on 9 different undirected graphs, the proposed algorithm has not only successfully found the shortest path in all, but did so by reducing the time by 60% and requiring less memory.

• Management Science and Financial Engineering
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• v.4 no.2
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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.

• The KIPS Transactions:PartA
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• v.8A no.2
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• pp.179-188
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• 2001

We analyze the property of candidate node set in the network graph, and propose an algorithm to decrease shortest path-finding computation time by using multiple dynamic-range queue(MDRQ) structure. This MDRQ structure is newly created for effective management of the candidate node set. The MDRQ algorithm is the shortest path-finding algorithm that varies range and size of queue to be used in managing candidate node set, in considering the properties that distribution of candidate node set is constant and size of candidate node set rapidly change. This algorithm belongs to label-correcting algorithm class. Nevertheless, because re-entering of candidate node can be decreased, the shortest path-finding computation time is noticeably decreased. Through the experiment, the MDRQ algorithm is same or superior to the other label-correcting algorithms in the graph which re-entering of candidate node didn’t frequently happened. Moreover the MDRQ algorithm is superior to the other label-correcting algorithms and is about 20 percent superior to the other label-setting algorithms in the graph which re-entering of candidate node frequently happened.