V. Melkonian and  E. Tardos, Approximation algorithms for a directed network design problem, IPCO '99.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... specialized connectivity problems of constructing a minimum cost uniformly k connected graph, the best known approximation guarantee is roughly factor k [3, 13] 1 If c is a metric, then there are constant factor approx imations for uniform k connectivity [12, 13] Last IPCO, Melkonian and Tardos [14] extend Jain s iterative rounding analysis to obtain a 4 approximation for uniform k edge connectivity on directed graphs. They also describe a different approach that yields a 2 approximation. There are numerous approximation results for other special cases of vertex and edge connectivity. For ....

V. Melkonian and E. Taxdos. Approximation algorithms for a directed network design problem. In 7th International Integer Programming and Combinatorial Optimization Conference, pages 345-360, 1999.

....at an arbitrary node v [5] Frank [6] showed that in the special case where the requirement function is also intersecting supermodular, i.e. the above inequality holds whenever X and Y intersect, the network design problem can be solved optimally in polynomial time. Melkonian and Tardos 1 [17] have recently shown that this result can be used to obtain a 2 approximation algorithm for any requirement function which is crossing supermodular. In undirected graphs, weakly supermodular functions have been widely studied as they model a broad class of network design problems, including for ....

....much better understood than their directed counterparts. In particular, techniques for network design problems on undirected graphs, e.g. the widely used primal dual approach [1, 10] do not seem to be easily amenable to directed network design problems. A recent result of Melkonian and Tardos[17] gives a directed graph analog of Jain s result and requires significant further insight into the combinatorial structure of basic solutions. They show that every basic solution to an LP relaxation of the design problem contains a variable of value at least a quarter whenever the requirement ....

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V. Melkonian and ' E. Tardos, Approximation algorithms for a directed network design problem, IPCO '99. Proceedings of the 7th International Integer Programming and Combinatorial Optimization Conference (IPCO) (1999).

....one needs to carry out a more profound study of the problem structure. A heaven sent opportunity is provided by some speci c properties of basic optimal solutions to a linear relaxation of the problem (Theorem 1) At this point we should notice the papers of Jain [6] and Melkonian and Tardos [7] where exploiting structural properties of basic solutions was also crucial in designing better approximations for some network design problems. The resulting algorithm (DIRCUT) is of rounding type and as such consists of two phases: the rst phase is to nd an optimal (fractional) solution to a ....

V. Melkonian and  E. Tardos, Approximation algorithms for a directed network design problem, Lecture Notes in Computer Science (Proceedings of IPCO'99) 1610 (1999), 345-360.

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V. Melkonian and  E. Tardos, Approximation algorithms for a directed network design problem, IPCO '99.

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V. Melkonian and  E. Tardos, Approximation algorithms for a directed network design problem, in IPCO'99, G. Cornuejols, R. E. Burcard, and G. J. Woeginger, eds., Lecture Notes in Comput. Sci. 1610, Springer-Verlag, New-York, 1999, pp. 345-360.

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