相关论文: Algorithms and Complexity for Variants of Covariat…

We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…

This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…

We show that the existence of a computationally efficient calibration algorithm, with a low weak calibration rate, would imply the existence of an efficient algorithm for computing approximate Nash equilibria - thus implying the unlikely…

Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…

In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…

We consider the problem of network coding across multiple unicasts. We give, for wired and wireless networks, efficient polynomial time algorithms for finding optimal network codes within the class of network codes restricted to XOR coding…

We design a fast algorithm that computes, for a given linear differential operator with coefficients in $Z[x ]$, all the characteristic polynomials of its p-curvatures, for all primes $p < N$ , in asymptotically quasi-linear bit complexity…

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…

Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…

We introduce the quadratic balanced optimization problem (QBOP) which can be used to model equitable distribution of resources with pairwise interaction. QBOP is strongly NP-hard even if the family of feasible solutions has a very simple…

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…

A Variable Parameter (VP) analysis, that we introduce here, aims to give a precise algorithm time complexity expression in which an exponent appears solely in terms of a variable parameter. A variable parameter is the number of objects with…

The theoretical aspects of four integer factorization algorithms are discussed in details in this note. The focus is on the performances of these algorithms on the subset of hard to factor balanced integers N = pq, p < q < 2p. The running…

We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…

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…

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…

The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent…

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where…

Cs\'{a}ji, Jungers, and Blondel prove that while a PageRank optimization problem with edge selection constraints is NP-hard, it can be solved optimally in polynomial time for the unconstrained case. This theoretical result is accompanied by…