Related papers: Perron-based algorithms for the multilinear pagera…
In this paper, we tackle the problem of computing a sequence of rankings with the guarantee of the Pareto-optimal balance between (1) maximizing the utility of the consumers and (2) minimizing unfairness between producers of the items. Such…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
In the search engine of Google, the PageRank algorithm plays a crucial role in ranking the search results. The algorithm quantifies the importance of each web page based on the link structure of the web. We first provide an overview of the…
PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…
PageRank is a ranking of the web pages that measures how often a given web page is visited by a random surfer on the web graph, for a simple model of web surfing. It seems realistic that PageRank may also have an influence on the behavior…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
PageRank is a well-known centrality measure for the web used in search engines, representing the importance of each web page. In this paper, we follow the line of recent research on the development of distributed algorithms for computation…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a…
A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlinear problems are associated with the minimization of a…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
The Perron-Frobenius theory for nonnegative matrices has been generalized to order-preserving homogeneous mappings on a cone and more recently to nonnegative multilinear forms. We unify both approaches by introducing the concept of…
The significance of the PageRank algorithm in shaping the modern Internet cannot be overstated, and its Complex Network theory foundations continue to be a subject of research. In this article we carry out a systematic study of the…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview…
In this article, we consider eigenvector centrality for the nodes of a graph and study the robustness (and stability) of this popular centrality measure. For a given weighted graph {\mathcal G} (both directed and undirected), we consider…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
The purpose of the research is to find a centrality measure that can be used in place of PageRank and to find out the conditions where we can use it in place of PageRank. After analysis and comparison of graphs with a large number of nodes…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…