By Per Austrin, Ryan O’Donnell, John Wright (auth.), Anupam Gupta, Klaus Jansen, José Rolim, Rocco Servedio (eds.)

This publication constitutes the joint refereed lawsuits of the fifteenth overseas Workshop on Approximation Algorithms for Combinatorial Optimization difficulties, APPROX 2012, and the sixteenth foreign Workshop on Randomization and Computation, RANDOM 2012, held in Cambridge, Massachusetts, united states, in August 2011. the quantity includes 28 contributed papers, chosen through the APPROX software Committee out of 70 submissions, and 28 contributed papers, chosen by way of the RANDOM application Committee out of sixty seven submissions. APPROX specializes in algorithmic and complexity matters surrounding the advance of effective approximate options to computationally tricky difficulties. RANDOM is worried with functions of randomness to computational and combinatorial problems.

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**Extra info for Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Cambridge, MA, USA, August 15-17, 2012. Proceedings**

**Sample text**

4. A good coordinate i and a bad coordinate i cannot define the same cut. Additive Approximation for Near-Perfect Phylogeny Construction 29 It immediately follows from Fact 1 that for a given good coordinate i one can eﬃciently reconstruct the endpoints of the edge on which i mutates, except for at most q coordinates. This leads us to the following deﬁnition. e. vi ’s, of the coordinates in Di . The pair (Di , bi ) is called the pattern of coordinate i. That set of terminals that match the pattern of i is the set Pbi = {x ∈ P : ∀j ∈ Di , xj = bij }.

Rounding Semideﬁnite Programming Hierarchies via Global Correlation. In: FOCS, pp. : Treewidth: Structure and Algorithms. , Zaks, S. ) SIROCCO 2007. LNCS, vol. 4474, pp. 11–25. : A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth. SIAM J. Comput. : Discovering Treewidth. , S´ ykora, O. ) SOFSEM 2005. LNCS, vol. 3381, pp. 1–16. : Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. : l22 spreading metrics for vertex ordering problems. : Graph Rewriting: An Algebraic and Logic Approach.

Let us now return to the problems discussed in the previous sections. It should not be surprising that the one-shot black pebbling problem is equivalent to a graph layout problem: the one-shot constraint reduces the problem to determining in which order to pebble the vertices; such an ordering induces a pebbling strategy in an obvious way. For the black-white case, it is known that the oneshot black-white pebbling cost of D is interreducible with a layout problem on an undirected graph G. 6. Turning to the width parameters, treewidth is equivalent to a graph layout problem called elimination width.