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By Hyung-Chan An, Robert D. Kleinberg, David B. Shmoys (auth.), Maria Serna, Ronen Shaltiel, Klaus Jansen, José Rolim (eds.)

This e-book constitutes the joint refereed court cases of the thirteenth foreign Workshop on Approximation Algorithms for Combinatorial Optimization difficulties, APPROX 2010, and the 14th overseas Workshop on Randomization and Computation, RANDOM 2010, held in Barcelona, Spain, in September 2010. The 28 revised complete papers of the APPROX 2010 workshop and the 29 revised complete papers of the RANDOM 2010 workshop incorporated during this quantity, have been conscientiously reviewed and chosen from sixty six and sixty one submissions, respectively. APPROX specializes in algorithmic and complexity concerns surrounding the advance of effective approximate options to computationally tough difficulties. RANDOM is worried with functions of randomness to computational and combinatorial difficulties.

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Read Online or Download Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 13th International Workshop, APPROX 2010, and 14th International Workshop, RANDOM 2010, Barcelona, Spain, September 1-3, 2010. Proceedings PDF

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Additional info for Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 13th International Workshop, APPROX 2010, and 14th International Workshop, RANDOM 2010, Barcelona, Spain, September 1-3, 2010. Proceedings

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Springer, Heidelberg (2007) 11. : On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks 12, 23–39 (1982) 12. 0941 (2009) 13. : Polylogarithmic inapproximability. In: STOC, pp. 585–594 (2003) 14. : The traveling-salesman problem and minimum spanning trees. Oper. Res. 18, 1138–1162 (1970) 15. : Poly-logarithmic approximation algorithms for directed vehicle routing problems. P. ) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 257–270. edu Abstract.

The undirected version of the Orienteering problem has also been studied extensively. The first constant factor approximation algorithm, due to Blum et al. [4], achieved a factor 4 approximation, and was later improved by Bansal et al. [2] to factor 3. The best currently known approximation algorithm, due to Chekuri, Korula and Pál [7], gives a factor (2 + ) approximation. On the negative side, the basic Orienteering problem is known to be APX-hard for both directed and undirected graphs [4]. Chekuri and Pál [8] have shown that an α-approximation for undirected Submodular Orienteering implies an O(α log k)-approximation for the Group Steiner tree problem, and therefore undirected Submodular Orienteering is hard to approximate to within factor Ω(log1− n) unless NP ⊆ ZTIME npoly log(n) [13].

Then for every function f : {0, 1}k → R+ and ε > 0, given a Max CSP+ (f ) instance F : {0, 1}n → R+ it is UG-hard to distinguish between the cases: Yes: There is an S ⊆ X such that F (S) ≥ cμ (f ) − ε. No: For every S ⊆ X it holds that F (S) ≤ s(f ) + ε. The proof of Theorem 3 follows the proof of [2] almost exactly. A proof can be found in the full version of this paper [1]. Consequently, for any submodular function f and pairwise independent distribution μ with all marginals equal, it is UG-hard to approximate Max CSP+ (f ) to within a factor s(f )/cμ (f )+ε for every ε > 0.

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