相关论文: Survey propagation: an algorithm for satisfiabilit…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. For random $k$-SAT and related models it happens at clause density $\alpha$…
The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these…
There has been much recent interest in the satisfiability of random Boolean formulas. A random k-SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
Much of the recent work on random constraint satisfaction problems has been inspired by ingenious but non-rigorous approaches from physics. The physics predictions typically come in the form of distributional fixed point problems that are…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
Many procedures for SAT and SAT-related problems -- in particular for those requiring the complete enumeration of satisfying truth assignments -- rely their efficiency on the detection of partial assignments satisfying an input formula. In…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships,…
In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These…
Functional verification constitutes one of the most challenging tasks in the development of modern hardware systems, and simulation-based verification techniques dominate the functional verification landscape. A dominant paradigm in…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random $k$-SAT model well for all clause/variable densities and all inverse…