Algorithmic version of the local lemma

Improved algorithmic versions of the Lovász Local Lemma

The Lovász Local Lemma is a powerful tool in combinatorics and computer science. The original version of the lemma was nonconstructive, and efficient algorithmic versions have been developed by Beck, Alon, Molloy & Reed, et al. In particular, the work of Molloy & Reed lets us automatically extract efficient versions of essentially any application of the symmetric version of the Local Lemma. How...

An Algorithmic Proof of the Lopsided Lovász Local Lemma (simplified and condensed into lecture notes)

For any probability space and a collection of events we give an algorithmic proof of the Lovász Local Lemma if there is a resampling oracle for each event. The resampling oracles act as an abstraction layer that isolates the details of the proof from the details of the probability space. The number of resamplings performed by the algorithm is bounded by expressions similar to those obtained by ...

A (1+epsilon)-approximation algorithm for partitioning hypergraphs using a new algorithmic version of the Lovász Local Lemma

Lecture 10 – Algorithmic version of the local lemma

1 The local lemma Let A be a collection of random events A 1. .. A m. For event A i , let Γ(A i) be a minimal set of events that A i depends on in the sense that A i is independent of all events in A \ {Γ(A i) ∪ A i } (information on events not in Γ(A i) ∪ A i does not affect the probability of event A i happening). The general version of the Lovasz local lemma [4] (see also [1]) is as follows....

A parallel algorithmic version of the Local Lemma

The Lovász Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of l...

Fuzzy Linear Programming and its Application for a Constructive Proof of a Fuzzy Version of Farkas Lemma

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.