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

This e-book constitutes the joint refereed lawsuits of the 14th overseas Workshop on Approximation Algorithms for Combinatorial Optimization difficulties, APPROX 2011, and the fifteenth overseas Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, united states, in August 2011.

The quantity provides 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 conscientiously reviewed and chosen for inclusion within the e-book. moreover abstracts of invited talks are included.

APPROX makes a speciality of algorithmic and complexity concerns surrounding the advance of effective approximate strategies to computationally tough difficulties. RANDOM is anxious with purposes of randomness to computational and combinatorial problems.

**Read or Download 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 PDF**

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**Extra resources 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**

**Example text**

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. The code C has a constant rate and constant fractional distance.

3760. Research supported by NSERC. This work was done while the third author was at the University of Toronto. A. Goldberg et al. ): APPROX/RANDOM 2011, LNCS 6845, pp. 13–25, 2011. c Springer-Verlag Berlin Heidelberg 2011 14 P. Austrin, M. Braverman, and E. Chlamt´ aˇc that even for two-player (bimatrix) games, the problem of computing a Nash equilibrium is PPAD-complete, thus unlikely to be solvable in polynomial time. Therefore, it makes sense to consider the complexity of approximate equilibria.

Then there exists a solution (A, R) to SRPSK2 with parameters (n, s, k, ) that uses O(m(s, k, Θ( ))) measurements. Moreover, if A has, in expectation, h(n, k, ) non-zeros per column, and the NSR2 recovery time is t(n, k, ), then A has, in expectation, O(h(s, k, Θ( ))) non-zeros, and R runs in O(t(s, k, Θ( ))) time3 . By a modiﬁcation of the algorithm of [15], we prove the following result: Lemma 7. 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.