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By Ashkan Aazami, Joseph Cheriyan, Krishnam Raju Jampani (auth.), Irit Dinur, Klaus Jansen, Joseph Naor, José Rolim (eds.)

This booklet constitutes the joint refereed court cases of the twelfth overseas Workshop on Approximation Algorithms for Combinatorial Optimization difficulties, APPROX 2009, and the thirteenth overseas Workshop on Randomization and Computation, RANDOM 2009, held in Berkeley, CA, united states, in August 2009.

The 25 revised complete papers of the APPROX 2009 workshop and the 28 revised complete papers of the RANDOM 2009 workshop integrated during this quantity, have been rigorously reviewed and chosen from fifty six and fifty eight submissions, respectively. APPROX makes a speciality of algorithmic and complexity concerns surrounding the improvement of effective approximate strategies to computationally tough difficulties. RANDOM is anxious with purposes of randomness to computational and combinatorial difficulties.

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Extra info for Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 12th International Workshop, APPROX 2009, and 13th International Workshop, RANDOM 2009, Berkeley, CA, USA, August 21-23, 2009. Proceedings

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The unaligned spillage problem is NP-complete even for chordal graphs. There is no o(log |V |)-approximation unless N P ⊆ DP T IM E(nO(log n) ). Proof. This can be shown via a simple approximation-preserving reduction from set cover. Suppose we would like to solve a set cover instance with n elements and m sets. We create a vertex for each of the m sets, and connect all of these vertices into a clique. For each element x we create m + 1 − δ(x) vertices, where δ(x) is the number of sets containing x.

Approximation algorithms for metric facility loca- tion and k-median problems using the primal-dual schema and Lagrangian relaxation. : A local search approximation algorithm for k-means clustering. : A simple linear time (1 + )- approximation algorithm for k-means clustering in any dimensions. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. : Least squares quantization in pcm. : On approximate geometric k-clustering. : Online facility location. : The planar k-means problem is NP-hard.

In this paper we are primarily interested in UFP instances that do not necessarily satisfy the no-bottleneck assumption. UCUFP and UFP-NBA have many applications and are of interest in themselves. However, the general UFP, due to algorithmic difficulties, has received less attention. One can extend some results for MEDP and UFP-NBA to UFP by separately considering requests that are within say a factor of 2 of each other; this geometric grouping incurs an additional factor of log dmax /dmin in the approximation ratio, which could be as large as a factor of n [18].

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