We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A major contribution of this paper is the development of a strongly polynomial-time 4/3-approximation algorithm for the problem. Specifically, we show that a linear programming relaxation of the problem is half-integral, and that the half-integral optimal solution can be rounded to a 4/3-approximate solution. We also prove that the linear programming relaxation of the problem with the edge-connectivity constraints is equivalent to minimizing the cost of half-integral multiflows that satisfy flow demands given from terminals. This observation implies a strongly polynomial-time algorithm for computing a minimum cost half-integral multiflow under flow demand constraints.
@InProceedings{fukunaga:LIPIcs.STACS.2015.316, author = {Fukunaga, Takuro}, title = {{Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation}}, booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)}, pages = {316--328}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-78-1}, ISSN = {1868-8969}, year = {2015}, volume = {30}, editor = {Mayr, Ernst W. and Ollinger, Nicolas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.316}, URN = {urn:nbn:de:0030-drops-49236}, doi = {10.4230/LIPIcs.STACS.2015.316}, annote = {Keywords: survivable network design, multiflow, LP rounding} }
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