• 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 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.

• 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.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9B
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• pp.751-759
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• 2008

Carrier Ethernet backbone network integrates distributed layer-2 based metro networks. In this networks, Multiple Spanning Tree Protocol (MSTP) has been uscd as a main routing protocol that allows multiple spanning trees in a network. A better routing protocol called IEEE802.1aq - Shortest Path Bridging (SPB) is recently proposed, that generates the shortest spanning tree per a destination node. As SPB provides a routing path per a destination node, there is no way to adapt network traffic at normal condition. If we are free from the principle of "a spanning tree per a destination node", we can achieve adaptive routing. Based on this philosophy, we propose a new spanning tree based protocol - Edge Node Divided Spanning Tree (ENDIST). ENDIST divides an edge node into sub-nodes as many as connecting links from the node and each sub-node generates a single shortest path tree based on SPB. Depending on network or nodal status, ENDIST chooses a better routing path by flow-basis. This added traffic engineering ability contributes to enhanced throughput and reduced delay in backbone networks. The simulation informs us that ENDIST's throughput under heavy load performs about 3.4-5.8 and 1.5-2.0 times compared with STP's and SPB's one respectively. Also, we verified that ENDIST's throughput corresponds to the theoretical upper bound at half of cases we investigated. This means that the proposed ENDIST is a dramatically enhanced and the close-to-perfect spanning tree based routing schemes.

• The KIPS Transactions:PartC
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• v.16C no.1
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• pp.83-90
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• 2009

Wireless Sensor Network (WSN) is a wireless network that gathers information from remote area with autonomously configured routing path. We propose a fusion based routing for a 'convergecast' in which all sensors periodically forward collected data to a base station. Previous researches dealt with only full-fusion or no-fusion case. Our Fusion rate based Spanning Tree (FST) can provide effective routing topology in terms of total cost according to all ranges of fusion rate f ($0{\leq}f{\leq}1$). FST is optimum for convergecast in case of no-fusion (f = 0) and full-fusion (f = 1) and outperforms the Shortest Path spanning Tree (SPT) or Minimum Spanning Tree (MST) for any range of f (0 < f < 1). Simulation of 100-node WSN shows that the total length of FST is shorter than MST and SPT nearby 31% and 8% respectively in terms of topology lengths for all range of f. As a result, we confirmed that FST is a very useful WSN topology.

• 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 Institute of Control, Robotics and Systems
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• v.18 no.12
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• pp.1096-1100
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• 2012

Most of previous genetic algorithms for solving graph problems have used a vertex-based encoding. We proposed an edge encoding based new genetic algorithm using a spanning tree. Contrary to general edge-based encoding, a spanning tree-based encoding represents only feasible partitions. As a target problem, we adopted the MAX CUT problem, which is well known as a representative NP-hard problem, and examined the performance of the proposed genetic algorithm. The experiments on benchmark graphs are executed and compared with vertex-based encoding. Performance improvements of the spanning tree-based encoding on sparse graphs was observed.

• 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.