• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.9-15
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• 2013

An inverse minimum spanning tree problem makes the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the concept of uncertain ${\alpha}$-minimum spanning tree is initiated for minimum spanning tree problem with uncertain edge weights. Using different decision criteria, two uncertain programming models are presented to formulate a specific inverse minimum spanning tree problem with uncertain edge weights involving a sum-type model and a minimax-type model. By means of the operational law of independent uncertain variables, the two uncertain programming models are transformed to their equivalent deterministic models which can be solved by classic optimization methods. Finally, some numerical examples on a traffic network reconstruction problem are put forward to illustrate the effectiveness of the proposed models.

• Journal of the Korea Society of Computer and Information
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• v.19 no.1
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• pp.57-64
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• 2014

As Steiner minimum tree building belongs to NP-Complete problem domain, heuristics for the problem ask for immense amount execution time and computations in numerous inputs. In this paper, we propose an efficient mechanism of euclidean Steiner minimum tree construction for numerous inputs using combination of Delaunay triangulation and Prim's minimum spanning tree algorithm. Trees built by proposed mechanism are compared respectively with the Prim's minimum spanning tree and minimums spanning tree based Steiner minimum tree. For 30,000 input nodes, Steiner minimum tree by proposed mechanism shows about 2.1% tree length less and 138.2% execution time more than minimum spanning tree, and does about 0.013% tree length less and 18.9% execution time less than minimum spanning tree based Steiner minimum tree in experimental results. Therefore the proposed mechanism can work moderately well to many useful applications where execution time is not critical but reduction of tree length is a key factor.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.283-293
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• 2010

In this paper, inverse constrained minimum spanning tree problem under Hamming distance. Such an inverse problem is to modify the weights with bound constrains so that a given feasible solution becomes an optimal solution, and the deviation of the weights, measured by the weighted Hamming distance, is minimum. We present a strongly polynomial time algorithm to solve the inverse constrained minimum spanning tree problem under Hamming distance.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.5_6
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• pp.319-323
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• 2003

Let P be a set of n points in the plane. A minimum spanning tree(MST) is a spanning tree connecting n points of P such that the sum of lengths of edges of the tree is minimized. A diameter of a tree is the maximum length of paths connecting two points of a spanning tree of P. The problem considered in this paper is to compute the spanning tree whose diameter is minimized over all spanning trees of P. We call such tree a minimum-diameter spanning tree(MDST). The best known previous algorithm[3] finds MDST in $O(n^2)$ time. In this paper, we suggest an approximation algorithm to compute a spanning tree whose diameter is no more than 5/4 times that of MDST, running in O(n$^2$log$^2$n) time. This is the first approximation algorithm on the MDST problem.

• Management Science and Financial Engineering
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• v.20 no.1
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• pp.17-19
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• 2014

In this paper, we consider an interesting variant of the inverse minimum traveling salesman problem. Given an instance (G, w) of the minimum traveling salesman problem defined on a metric space, we fix a specified Hamiltonian cycle $HC_0$. The task is then to adjust the edge cost vector w to w' so that the new cost vector w' satisfies the triangle inequality condition and $HC_0$ can be returned by the minimum spanning tree algorithm in the TSP-instance defined with w'. The objective is to minimize the total deviation between the original and the new cost vectors with respect to the $L_1$-norm. We call this problem the inverse metric traveling salesman problem against the minimum spanning tree algorithm and show that it is closely related to the inverse metric spanning tree problem.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.1
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• pp.10-19
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• 2005

The minimum spanning tree (MST) problem is one of the traditional optimization problems. Unlike the MST, the degree constrained minimum spanning tree (DCMST) of a graph cannot, in general, be found using a polynomial time algorithm. So, finding the DCMST of a graph is a well-known NP-hard problem of importance in communications network design, road network design and other network-related problems. So, it seems to be natural to use evolutionary algorithms for solving DCMST. Especially, when applying an evolutionary algorithm to spanning tree problems, a representation and search operators should be considered simultaneously. This paper introduces a new tree representation scheme and a genetic operator for solving combinatorial tree problem using evolutionary algorithms. We performed empirical comparisons with other tree representations on several test instances and could confirm that the proposed method is superior to other tree representations. Even it is superior to edge set representation which is known as the best algorithm.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.509-518
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• 2009

In this paper, a mechanism that produces an approximation edges minimum spanning tree swiftly using virtual nodes called portals dividing given edges into same distance sub-edges. The approximation edges minimum spanning tree can be used in many useful areas as connecting communication lines, road networks and railroad systems. For 3000 random input edges, when portal distance is 0.3, tree building time decreased 29.74% while the length of the produced tree increased 1.8% comparing with optimal edge minimum spanning tree in our experiment. When portal distance is 0.75, tree building time decreased 39.96% while the tree length increased 2.96%. The result shows this mechanism might be well applied to the applications that may allow a little length overhead, but should produce an edge connecting tree in short time. And the proposed mechanism can produce an approximation edge minimum spanning tree focusing on tree length or on building time to meet user requests by adjusting portal distance or portal discard ratio as parameter.

• IE interfaces
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• v.15 no.3
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• pp.241-246
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• 2002

Some extensions of minimum spanning tree problem are NP-hard problem in which polynomial-time solutions for them do not exist. Because of their complexity, recently some researcher have used the genetic algorithms to solve them. In genetic algorithm approach the Prufer number is usually used to represent a tree. In this paper we discuss the problem of the Prufer number encoding method and propose an improved genetic operation. Using a numerical comparison we demonstrate the excellence of the proposed method.

• Journal of the Korea Society of Computer and Information
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• v.17 no.1
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• pp.161-169
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• 2012

In general, Euclidean minimum spanning tree is a tree connecting input nodes with minimum connecting cost. But the tree may not be optimal when applied to real world problems of three dimension. In this paper, three dimension Euclidean minimum spanning tree is proposed, connecting all input nodes of 3-dimensional space with minimum cost. In experiments for 30,000 input nodes with 100% space ratio, the tree produced by the proposed method can reduce 90.0% connection cost tree, compared with the tree by two dimension Prim's minimum spanning tree. In two dimension plane, the proposed tree increases 251.2% connecting cost, which is pointless in 3-dimensional real world. Therefore, the proposed method can work well for many connecting problems in real world space of three dimensions.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.29 no.2
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• pp.33-39
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• 2015

Power supplying capacity of the distribution feeder should be maintained within thermal capacity of the wire. This paper presents the minimum spanning tree based load balancing technique to release multiple overloading of distribution feeders. In order to minimize number of involved backup feeders, Dijkstra and Prim algorithm are adopted to construct minimum spanning tree. Simulation testing result based on part of KEPCO's commercial distribution systems shows effectiveness of proposed scheme.