| K. U. Drangmeister, S. O. Krumke, M. V. Marathe, H. Noltemeier and S. S. Ravi, Modifying edges of a network to obtain short subgraphs, Theoretical Computer Science 203, 1998, 91 - 121. |
....B, TU Graz, Steyrergasse 30, A 8010 Graz, Austria. linyixun mail.zzu.edu.cn Department of Mathematics, Zhengzhou University, Zhengzhou, China. mazhang cityu.hk.edu. Department of Mathematics, City University of Hong Kong, Hong Kong. 1 as by Drangmeister, Krumke, Marathe, Noltemeier and Ravi [5]. Phillips [13] modi es maximum ows subject to budget constraints. Related to these improvement models subject to budget constraints are so called inverse optimization models. In an inverse optimization model the parameter should be changed as little as possible such that speci ed solutions ....
K. U. Drangmeister, S. O. Krumke, M. V. Marathe, H. Noltemeier and S. S. Ravi, Modifying edges of a network to obtain short subgraphs, Theoretical Computer Science 203, 1998, 91 - 121.
.... in this eld, which includes the shortest path problem (see for instance Fulkerson and Harding [55] the minimum spanning tree problem (see for instance Frederickson and Solis Oba [54, 53] Krumke, Marathe, Noltemeier, Ravi, and Ravi [60] Drangmeister, Krumke, Marathe, Noltemeier, Ravi [48]) maximum ow problems (see for instance Phillips [64] bottleneck capacity expansion problems (see Yang and Zhang [69] Zhang, Yang, and Lin [70] and Burkard, Klinz, and Zhang [46] and weight reduction problems (see Burkard, Lin, and Zhang [47] 3 Methods This section presents some of the ....
K. U. Drangmeister, S. O. Krumke, M. V. Marathe, H. Noltemeier, and S. S. Ravi, Modifying edges of a network to obtain short subgraphs, Theoret. Comput. Sci. 203 (1998), 91-121.
....the capacity (weight) of the structure (E; F ) Typically, these problems involve lower bounds on the new capacities (weights) which turns most of them into NP hard problems. See e.g. Philipps [12] for the maximum ow minimum cut case and Drangmeister, Krumke, Marathe, Noltemeier and S.S. Ravi [5] for the minimum spanning tree case. The paper by Krumke, Marathe, Noltemeier, R. Ravi and S.S. Ravi [9] is worth to be mentioned here since it considers multi criteria budget constraints (such constraints can be formulated within the framework of our algebraic model) 2.4 Parametric ....
K.U. Drangmeister, S.O. Krumke, M.V. Marathe, H. Noltemeier and S.S. Ravi, Modifying edges of a network to obtain short subgraphs, Theoretical Computer Science 203, 1998, 91-121.
....Di(T) we denote the diameter of T with respect to the length function l, i.e. the length of a longest path in T. We consider two closely related diameter lowering problems (for motivations, variants, complexity issues and approximation algorithms for this kind of problems on general networks see [1, 2]) PROBLEM DLP(T,l,c,D) Given 0 D D, find the reals 0 x(e) e) e E, such that the tree obtained from T by decreasing the length of every edge e E by x(e) units has diameter at most D and the cost ecE c(e) x(e) of this lowering is minimized. PROBLEM DLP(T, l, c, B) Given a budget B ....
K.U. Drangmeister, S.O. Krumke, M.V. Marathe, H. Noltemeier, and S.S. Ravi, Mod- ifying edges of a network to obtain short subgraphs, Theoretical Computer Science 203(999).
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