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12. R. Krishnan and B. Raghavachari. The directed minimum degree spanning tree problem. In FSTTCS, pages 232–243, 2001. 13. C. H. Papadimitriou and U. Vazirani. On two geometric problems related to the traveling salesman problem. J. Algorithms, 5:231–246, 1984. 14. R. Ravi, M. V. Marathe, S. S. Ravi, D. J. Rosenkrantz, and H. B. Hunt, III. Many birds with one stone: multi-objective approximation algorithms. In Proceedings of ACM STOC,1993. 15. R. Ravi, M. V. Marathe, S. S. Ravi, D. J. Rosenkrantz, and H.

M the edges ei , ei+1 are twins. By definition, any edge e is parallel to itself and all edges parallel to e have the same length. Notice also that exactly two edges parallel to a given edge e belong to ∂P. We continue with the notion of generating set introduced in [5] and used in approximation algorithms from [1, 7]. A generating set is a subset F of pairs of terminals (or, more compactly, of their indices) with the property that a rectilinear network containing l1 -paths for all pairs in F is a Manhattan network on T.

Livnat, and U. Zwick. Improved rounding techniques for the MAX 2-SAT and MAX DI-CUT problems. In Proceedings of the 9th IPCO, Cambridge, Massachusetts, pages 67–82, 2002. [MM01a] S. Matuura and T. Matsui. 863-approximation algorithm for MAX DICUT. In Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques, Proceedongs of APPROX-RANDOM’01, Berkeley, California, pages 138–146, 2001. [MM01b] S. Matuura and T. Matsui. 935-approximation randomized algorithm for MAX 2SAT and its derandomization.

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