Unformatted text preview: Conditional Expetations. Let G be a simple graph with vertex set V and edge set E . A cut of a set of vertices V ⊆ V is the number of edges that have one endpoint in V and the other in V \ V . The NP-complete MaxCut problem asks for the largest cut. A simple randomized approximation problem works as follows: Throw for every vertex a coin. If we got “tails” we add it to V otherwise not. In the end an edge is with probability 1 / 2 in the cut, so the expected value of the cut for V is | E | / 2. Since every cut is at most | E | we have a 2-approximation. Use the concept of conditional expectations to de-randomize this algorithm. 1...
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- Fall '10
- Data Structures, Probability theory, Conditional expectation, Prof. Erik Demaine, Dr. Andr´ Schulz