• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.407-416
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• 1998

For fast Cholesky factorization, it is most important to reduce the number of nonzero elements by ordering methods. Generally, the minimum deficiency ordering produces less nonzero elements, but it is very slow. We propose an efficient implementation method. The minimum deficiency ordering requires much computations related to adjacent nodes. But, we reduce those computations by using indistinguishable nodes, the clique storage structures, and the explicit storage structures to compute deficiencies.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.386-393
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• 2003

For fast Cholesky factorization, it is most important to reduce the number of non-zero elements by ordering methods. Minimum deficiency ordering produces less non-zero elements. However, since it is very slow. the minimum degree algorithm is widely used. To improve the computation time, Rothberg's AMF uses an approximate deficiency instead of computing the deficiency. In this paper we present simple efficient methods to obtain a good approximate deficiency using information related to cliques. Experimental results show that our proposed method produces better ordering quality than that of AMF.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.3
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• pp.63-74
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• 1996

Ordering plays an important role in solving an LP problem with sparse matrix by the interior point method. Since ordering is NP-complete, we try to find an efficient method. The objective of this paper is to present an efficient heuristic ordering method for implementation of the minimum deficiency method. Both the ordering method and the data structure play important roles in implementation. First we define a new heuristic pseudo-deficiency ordering method and a data structure for the method-quotient graph and cliqued storage. Next we show an experimental result in terms of time and nonzero numbers by NETLIB problems.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.2
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• pp.99-104
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• 2024

In the deficiency of an exact solution yielding algorithm, approximate algorithms remain as a solely viable option to the Minimum Linear Arrangement(MinLA) problem of Binary tree. Despite repeated attempts by a number of algorithm on k = 10, only two of them have been successful in yielding the optimal solution of 3,696. This paper therefore proposes an algorithm of O(n) complexity that delivers the exact solution to the binary tree. The proposed algorithm firstly employs an In-order search method by which n = 2^k - 1 number of nodes are assigned with a distinct number. Then it reassigns the number of all nodes that occur on level 2 ≤ 𝑙 ≤ k-2, (k = 5) and 2 ≤ 𝑙 ≤ k-3, (k = 6), including that of child of leaf node. When applied to k=5,6,7, the proposed algorithm has proven Chung[14]'s S^(k)_min=2^k-1+4+S^(k-1)_min+2S^(k-2)_min conjecture and obtained a superior result. Moreover, on the contrary to existing algorithms, the proposed algorithm illustrates a detailed assignment method. Capable of expeditiously obtaining the optimal solution for the binary tree of k > 10, the proposed algorithm could replace the existing approximate algorithms.