Summary
In this paper we discuss some applications of Gass & Saaty’s parametric programming procedure (GSP3). This underutilized procedure is relevant to solution strategies for many problem types but is often not considered as a viable alternate approach. By demonstrating the utility of this procedure, we hope to attract other researchers to explore the use of GSP 3 as a solution approach for important problems in operations research, computer science, information systems, and other areas.
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References
V. Aggarwal. A Lagrangean-Relaxation Method for the Constrained Assignment Problem. Computers & Operations Research, 12:97–106, 1985.
C. Alpert and S. Yao. Spectral Partitioning: The More Eigenvectors, the Better. 32 nd ACM/IEEE Design Automation Conference, 195–200, 1995.
J. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York, NY, 1981.
H. Bock. Probability Models in Partitional Cluster Analysis. Computational Statistics and Data Analysis, 23:5–28, 1996.
K.-H. Borgwardt. The Average Number of Steps Required by the Simplex Method is Polynomial. Zeitchrift fur Operations Research, 26:157–177, 1982.
N. Bryson. Parametric Programming and Lagrangian Relaxation: The Case of the Network Problem with a Single Side-Constraint. Computers & Operations Research, 18:129–140, 1991.
N. Bryson. Applications of the Parametric Programming Procedure. European Journal of Operational Research, 54:66–73, 1991.
N. Bryson. Identifying the Efficient Extreme-Points of the Three-Objective Linear Programming Problem. Journal of the Operational Research Society, 44:81–85, 1993.
M-S. Chen and P. Yu. Optimal Design of Multiple Hash Tables for Concurrency Control. IEEE Transactions on Knowledge and Data Engineering, 9:384–390, 1997.
G. Dantzig. Making Progress during a Stall in the Simplex Algorithm. Technical Report SOL 88-5, Stanford University, Stanford, CA, 1988.
R. Dave. Generalized Fuzzy C-Shells Clustering and Detection of Circular and Elliptic Boundaries. Pattern Recognition, 25:713–722, 1992.
P. Denning. Working Sets Past and Present. IEEE Transactions on Software Engineering, 6:64–84, 1980.
I. Dhillon. Co-Clustering Documents and Words Using Bipartite Spectral Graph Partitioning. Proceedings of the 7th ACM SIGKDD, 269–274, 2001.
C. Ding and X. He. Linearized Cluster Assignment via Spectral Ordering. ACM Proceedings of the 21 st International Conference on Machine Learning, 30, 2004.
C. Faloutsos and K-I. Lin. FastMap: A Fast Algorithm for the Indexing, Data Mining, and Visualization of Traditional and Multimedia Datasets. ACM SIGMOD Proceedings, 163–174, 1995.
S. Gass and T. Saaty. The Computational Algorithm for the Parametric Objective Function. Naval Research Logistics Quarterly, 2:39–45, 1955.
L. Hagen and A. Kahng. New Spectral Methods for Ratio Cut Partitioning and Clustering. IEEE Trans. on Computed Aided Design, 11:1074–1085, 1992.
A. Joseph and N. Bryson. Partitioning of Sequentially Ordered Systems Using Linear Programming. Computers & Operations Research, 24:679–686, 1997a.
A. Joseph and N. Bryson. “Parametric Programming and Cluster Analysis”, European Journal of Operational Research 111:582–588, 1999.
A. Joseph and N. Bryson. W-Efficient Partitions and the Solution of the Sequential Clustering Problem. Annals of Operations Research: Nontraditional Approaches to Statistical Classification, 74:305–319, 1997b.
N. Karmarkar. A New Polynomial-Time Algorithm for Linear Programming. Combinatorica, 4:373–395,1984.
B. Kernighan. Optimal Sequential Partitions of Graphs. Journal of the Association for Computing Machinery, 18:34–40, 1971.
L. Kurgan and K. Cios. CAIM Discretization Algorithm. IEEE Transactions on Knowledge and Data Engineering, 16:145–153, 2004.
H. Liu and R. Setiono. Feature Selection by Discretization. IEEE Transactions on Knowledge and Data Engineering, 9:642–645, 1997.
T. Magnanti and J. Orlin. Parametric Linear Programming and Anti-Cycling Rules. Mathematical Programming, 41:317–325, 1988.
J. McQueen. Some Methods for Classification and Analysis of Multivariate Observations, In: Lecam, L.M. and Neyman, J. (Eds.): Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 281–297, 1967.
J. Moy, K. Lam, and E. Choo. Deriving Partial Values in MCDM by Goal Programming. Annals of Operations Research, 74:277–288, 1997.
F. Murtagh. A Survey of Recent Advances in Hierarchical Clustering Algorithms which Use Cluster Centers. Computer Journal, 26:354–359, 1983.
G. L. Nemhauser and L. A. Wolsey. Integer and Combinatorial Optimization. Wiley, New York, 1988.
K.-M. Osei-Bryson and A. Joseph. Applications of Sequential Set Partitioning: Three Technical Information Systems Problems. Omega, 34:492–500, 2006.
K.-M. Osei-Bryson and T. Inniss. A Hybrid Clustering Algorithm. Computers & Operations Research, in press, 2006.
L. Stanfel. Recursive Lagrangian Method for Clustering Problems. European Journal of Operational Research, 27:332–342, 1986.
J. Ward. Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association, 58:236–244, 1963.
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Osei-Bryson, KM. (2006). Toward Exposing the Applicability of Gass & Saaty’s Parametric Programming Procedure. In: Alt, F.B., Fu, M.C., Golden, B.L. (eds) Perspectives in Operations Research. Operations Research/Computer Science Interfaces Series, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39934-8_14
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DOI: https://doi.org/10.1007/978-0-387-39934-8_14
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