Graph algorithms

At the heart of every local search procedure is a directed graph on candidate solutions (states) such that every unsatisfying state has at least one outgoing arc. In randomized local search the hope is that a random walk on the graph reaches a satisfying state (sink) quickly. We give a general algorithmic local lemma by establishing a sufficient condition for this to be true. Our work is inspired by Moser's entropic method proof of the Lov'{a}sz Local Lemma (LLL) for satisfiability but completely bypasses the Probabilistic Method formulation of the LLL.

Although graphs and matrices are popular ways to model data drawn from
many application domains, the size scale, sparsity properties, noise
properties, and many other aspects of graphs and matrices arising in
realistic machine learning and data analysis applications present
fundamental challenges for traditional matrix and graph algorithms.
Informally, this at root has to do with the observation that small-scale
or local structure in many data sets is often better or more meaningful

Keywords: Online image processing, unsupervised algorithms, fast algorithms, color balance, screened Poisson equation, denoising, image comparison, Retinex theory, affine invariant SIFT

Abstract: This is a new concept of publication for image processing. Putting image processing and image analysis algorithms on line allows every researcher to test directly the algorithms on his (her) own images. Some sample images are also proposed on each algorithm site. This project is under construction, but several algorithms are already available at

An expression graph, informally speaking, represents a function in a
way that cam be manipulated to reveal various kinds of information
about the function, such as its value or partial derivatives at
specified arguments and bounds thereon in specified regions. (Various
representations are possible, and all are equivalent in complexity, in
that one can be converted to another in time linear in the
expression's size.) For mathematical programming problems, including