Abstract
We are interested in a situation where a large number of problems of some common type must be solved. The problems are defined on some space of “solutions”, share the same objective function to be optimized, and differ by their sets of constraints. Thus a solution may be feasible with respect to a set of problems and infeasible with respect to the others. We investigate the possibility of solving the problems simultaneously and presenting the optimal solutions compactly, so that each of these solutions can be easily obtained when needed.
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References
Bartholdi, J.J. (1982), “A Good Submatrix is Hard to Find”, Operations Research Letters 5, 190–193.
Berge, C. (1973), Graphs and Hypergraphs, North Holland Publishing Co., Amsterdam.
Cheng C.K. and T.C. Hu (1988), “Maximum Concurrent Flow and Minimum Ratio Cut”, Technical Report Number CS88-141, department of Computer Science and Engineering, University of California, San Diego, December 1988.
Conforti, M. and M.R. Rao (1987), “Some New Matroids on Graphs: Cut Sets and the Max Cut Problem”, Math. of Operations Research 12, 193–204.
Gomory, R.E., and T.C. Hu (1961), “Multi-Terminal Network Flows”, J. SIAM, 9, 551–570.
Granot, F. and R. Hassin (1986), “Multi-Terminal Maximum Flows in Node Capacitated Networks”, Discrete Applied Mathematics 13, 157–163.
Gusfield, D (1990), “Very Simple Methods for All Pairs Network Flow Analysis”, SIAM Journal on Computing 19, 143–155.
Gusfield, D., and D. Naor (1988), “Extracting Maximal Information on Sets of Minimum Cuts”, Computer Science Division, University of California, Davis.
Gusfield, D., and D. Naor (1990), “Efficient Algorithms for Generalized Cut Trees” Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms.
Hassin, R. (1988), “Solution Bases of Multiterminal Cut Problems”, Mathematics of Operations Research 13, 535–542.
Hassin, R. (1989), “Multiterminal Xcut Problems”, presented in the NATO Workshop on Topological Network Design, Copenhagen, June 1989.
Hassin, R. (1990), “An Algorithm for Computing Maximum Solution Bases”, Operations Research letters.
Hu, T.C. (1963), “Multi-Commodity Network Flows”, Operations Research 11, 344–360.
Katoh, N., T. Ibaraki, and H. Mine (1982), “An Efficient Algorithm for K Shortest Simple Paths”, Networks 12, 411–427.
Matula, D. (1987), “Determining Edge Connectivity in O(mn)”, Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, 249–251.
Picard, J.C., and M. Queyranne (1980), “On the Structure of All Minimum Cuts in a Network and Applications”, Mathematical Programming Study 13, 8–16.
Schnorr, C.P. (1976), “Bottlenecks and Edge Connectivity in Unsymmetrical Networks”, SIAM Journal on Computing 8, 265–274.
Yannakakis, M. (1981), “Node-deletion Problems on Bipartite Graphs”, SIAM Journal on Computing 10, 210–237.
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© 1990 Springer-Verlag Berlin Heidelberg
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Hassin, R. (1990). Simultaneous solution of families of problems. In: Asano, T., Ibaraki, T., Imai, H., Nishizeki, T. (eds) Algorithms. SIGAL 1990. Lecture Notes in Computer Science, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52921-7_78
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DOI: https://doi.org/10.1007/3-540-52921-7_78
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