相关论文: Exponentially hard problems are sometimes polynomi…

The analysis of the solving complexity of random 3-SAT instances using the Davis-Putnam-Loveland-Logemann (DPLL) algorithm slightly below threshold is presented. While finding a solution for such instances demands exponential effort with…

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…

Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…

An analysis of the average-case complexity of solving random 3-Satisfiability (SAT) instances with backtrack algorithms is presented. We first interpret previous rigorous works in a unifying framework based on the statistical physics…

Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such…

The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…

The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…

We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…

Randomized exponential backoff is a widely deployed technique for coordinating access to a shared resource. A good backoff protocol should, arguably, satisfy three natural properties: (i) it should provide constant throughput, wasting as…

The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We…

In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…

We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires…

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

In this note I will review some of the recent results that have been obtained in the probabilistic approach to the random satisfiability problem. At the present moment the results are only heuristic. In the case of the random…