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By Sanjeev Arora, Rong Ge (auth.), Leslie Ann Goldberg, Klaus Jansen, R. Ravi, José D. P. Rolim (eds.)

This booklet constitutes the joint refereed complaints of the 14th overseas Workshop on Approximation Algorithms for Combinatorial Optimization difficulties, APPROX 2011, and the fifteenth foreign Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, united states, in August 2011.
The quantity offers 29 revised complete papers of the APPROX 2011 workshop, chosen from sixty six submissions, and 29 revised complete papers of the RANDOM 2011 workshop, chosen from sixty four submissions. They have been rigorously reviewed and chosen for inclusion within the e-book. moreover abstracts of invited talks are included.
APPROX makes a speciality of algorithmic and complexity matters surrounding the advance of effective approximate options to computationally tricky difficulties. RANDOM is anxious with purposes of randomness to computational and combinatorial problems.

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Additional info for Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 14th International Workshop, APPROX 2011, and 15th International Workshop, RANDOM 2011, Princeton, NJ, USA, August 17-19, 2011. Proceedings

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There exist a distribution on m × n matrices A and a collection of algorithms {RS | S ∈ [n] } such that for any x ∈ Rn and set S ⊆ [n], |S| = s, s RS (Ax) recovers x ˆ with the guarantee that x−x ˆ 2 ≤ (1 + ) x − xS,k 2 (26) with probability 3/4. The matrix A has m = O((k/ ) log(s/k)) rows. Proof. To apply a NSR2 solution to SRPSK2 using Lem. 6, we need the columns of the measurement matrix to be generated independently. However, this requirement does not hold with the algorithm in [15] as is. Therefore, we show how to modify it to satisfy this requirement without changing its recovery properties and asymptotic number of measurements.

It will suffice for our purposes if the columns of each E (j) and each D(j) are independent. d. d. (to 1, −1 or 0). Thus, every entry, and therefore every column, of E (j) is already independent without modification. d. submatrices. d. (j) (j) (j) “blocks” B1 , B2 , . . , Bkcj , which will be the smallest unit of vertically stacked (j) submatrices we need to consider (see Fig. 1). Within each block Bi , each column is independently chosen to be non-zero with some probability, and the ith non-zero column is equal to the ith code word wi from some error-correcting code C.

Games and Econ. : How Hard Is It to Approximate the Best Nash Equilibrium?. SIAM J. Comput. : Playing large games using simple strategies. In: ACM Conference on Electronic Commerce, pp. : Small clique detection and approximate nash equilibria. , Rolim, J. ) APPROX 2009. LNCS, vol. 5687, pp. 673–685. : On the complexity of the parity argument and other inefficient proofs of existence. J. Comp. Sys. Sci. : An optimization approach for approximate nash equilibria. Internet Mathematics 5(4), 365–382 (2008) Sparse Recovery with Partial Support Knowledge Khanh Do Ba and Piotr Indyk Massachusetts Institute of Technology, Cambridge MA 02139, USA Abstract.

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