Non-independent randomized rounding and coloring

Non-independent randomized rounding and coloring

Structured Randomized Rounding and Coloring

Non-independent Randomized Rounding and an Application to Digital Halftoning

LP Relaxation , Rounding , and Randomized Rounding

1.1 Max-flow min-cut A flow network is a directed graph D = (V,E) with two distinguished vertices s and t called the source and the sink, respectively. Moreover, each arc (u, v) ∈ E has a certain capacity c(u, v) ≥ 0 assigned to it. Let X be a proper non-empty subset of V . Let X̄ := V −X , then the pair (X, X̄) forms a partition of V , called a cut of D. The set of arcs of D going from X to X̄ is...

Randomized Rounding

One of the key ideas in randomized algorithms is that good outcomes are likely enough to happen if we flip coins. This allows us to avoid distinguishing many cases and treating each separately. In this lecture, we will study one particular such technique, which allows us to design approximation algorithms. In all of our algorithms, we will rely on linear programs (LPs). The examples are selecte...