# CMU Randomized Algorithms

Randomized Algorithms, Carnegie Mellon: Spring 2011

## Lecture 1 notes and references

The reference to the best known algorithm for 3SAT we mentioned in class is this paper: Improving PPSZ for 3-SAT using Critical Variables, by Hertli, Moser, and Scheder.

It gives a algorithm with an expected runtime of 1.321^n, and the idea to cleverly combine Schoening’s algorithm (the one you saw today and will analyze in HW1) and a previous algorithm of Paturi, Pudlak, Saks and Zane (PPSZ).

At a super-high level, Schoening’s algorithm does better if there are lots of (well-separated) solutions that the randomized process can make a beeline for. The PPSZ algorithm, another very simple randomized algorithm that we may see in a later post, works better if there are few satisfying assignments. The idea in the paper of Hertli and others is how to trade off the two guarantees to do better than either one individually; this idea of combining Schoening and PPSZ goes back to a paper of Iwama and Tamaki (SODA ’04).

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