CASCADE RECTANGLE ALGORITHM AND TRANSPOSITION MATRIX IN THE CYCLED SHORTEST PATH NETWORKS

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AINI A.; ESHGHI K.

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Journal: Journal of Operational Research in its Applications Year:2018 | Volume:14 | Issue:4 (55) Page(s): 67-87

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Information Journal Paper

Title

CASCADE RECTANGLE ALGORITHM AND TRANSPOSITION MATRIX IN THE CYCLED SHORTEST PATH NETWORKS

Author(s)

AINI A. | ESHGHI K. | Issue Writer Certificate

Keywords

CYCLED SHORTEST PATH NETWORKS ALGORITHMSQ1

CASCADE RECANGLE ALGORITHMQ1

REVISED MATRIX METHODQ1

FLOYD-WARSHALL ALGORITHMQ1

REVISED CASCADE METHODQ1

Abstract

Shortest path problem is among the most interesting problems in the field of graph and network theory. There are many efficient matrices-based algorithms for detecting of shortest path and distance between all pairs of this problem in the literature of research. In this paper, a new exact algorithm, named the Cascade Rectangle Algorithm, is presented by using the main structure of previous exact algorithms and developing some new techniques. In cascade rectangle algorithm, all mathematical calculations and operations execute in multirectangle structure. This algorithm is an efficient exact algorithm with simple procedure and fast running time. Furthermore, a new matrix on the basis of route matrix, called the Transposition Matrix, is defined to apply the sensitivity analysis and reoptimization of the all pairs shortest path networks. Finally, one illustrative example is also solved in a step by step procedure to show the details of the cascade rectangle algorithm, FLOYD-WARSHALL ALGORITHM, revised matrix algorithm, and Transposition Matrix.

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APA: Copy

AINI, A., & ESHGHI, K.. (2018). CASCADE RECTANGLE ALGORITHM AND TRANSPOSITION MATRIX IN THE CYCLED SHORTEST PATH NETWORKS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 14(4 (55) ), 67-87. SID. https://sid.ir/paper/164517/en

Vancouver: Copy

AINI A., ESHGHI K.. CASCADE RECTANGLE ALGORITHM AND TRANSPOSITION MATRIX IN THE CYCLED SHORTEST PATH NETWORKS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)[Internet]. 2018;14(4 (55) ):67-87. Available from: https://sid.ir/paper/164517/en

IEEE: Copy

A. AINI, and K. ESHGHI, “CASCADE RECTANGLE ALGORITHM AND TRANSPOSITION MATRIX IN THE CYCLED SHORTEST PATH NETWORKS,” JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), vol. 14, no. 4 (55) , pp. 67–87, 2018, [Online]. Available: https://sid.ir/paper/164517/en

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