相关论文: The Distance Approach to Approximate Combinatorial…
In this paper, we propose a randomized $\tilde{O}(\mu(G))$-round algorithm for the maximum cardinality matching problem in the CONGEST model, where $\mu(G)$ means the maximum size of a matching of the input graph $G$. The proposed algorithm…
The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
This article presents an adaptive mean shift algorithm designed for datasets with varying local scale and cluster cardinality. Local distance distributions, from a point to all others, are used to estimate the cardinality of the local…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum-Shub-Smale model with square root. It…
Using purely combinatorial means we obtain results on simultaneous Diophantine approximation modulo 1 for systems of polynomials with real coefficients and no constant term.
The algorithm and complexity of approximating the permanent of a matrix is an extensively studied topic. Recently, its connection with quantum supremacy and more specifically BosonSampling draws special attention to the average-case…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
It is well known that, under very weak assumptions, multiobjective optimization problems admit $(1+\varepsilon,\dots,1+\varepsilon)$-approximation sets (also called $\varepsilon$-Pareto sets) of polynomial cardinality (in the size of the…
Celebrated work of Jerrum, Sinclair, and Vigoda has established that the permanent of a {0,1} matrix can be approximated in randomized polynomial time by using a rapidly mixing Markov chain. A separate strand of the literature has pursued…
We present a $(1- \varepsilon)$-approximation algorithms for maximum cardinality matchings in disk intersection graphs -- all with near linear running time. We also present estimation algorithm that returns $(1\pm…
We construct a deterministic approximation algorithm for computing a permanent of a $0,1$ $n$ by $n$ matrix to within a multiplicative factor $(1+\epsilon)^n$, for arbitrary $\epsilon>0$. When the graph underlying the matrix is a constant…
The success of Constraint Programming relies partly on the global constraints and implementation of the associated filtering algorithms. Recently, new ideas emerged to improve these implementations in practice, especially regarding the all…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon,n,\eta$ be the energy gap, the system size, and the desired precision, respectively.…
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications, including global optimization of polynomials and rational…