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We propose a simple and optimal algorithm, BackMC, for local PageRank estimation in undirected graphs: given an arbitrary target node $t$ in an undirected graph $G$ comprising $n$ nodes and $m$ edges, BackMC accurately estimates the…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable…
On the Web, visits of a page are often introduced by one or more valuable linking sources. Indeed, good back links are valuable resources for Web pages and sites. We propose to discovering and leveraging the best backlinks of pages for…
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
The advent of the internet, followed shortly by the social media made it ubiquitous in consuming and sharing information between anyone with access to it. The evolution in the consumption of media driven by this change, led to the emergence…
Given a large-scale graph with millions of nodes and edges, how to reveal macro patterns of interest, like cliques, bi-partite cores, stars, and chains? Furthermore, how to visualize such patterns altogether getting insights from the graph…
In recent work with Lins and Nussbaum the first author gave an algorithm that can detect the existence of a positive eigenvector for order-preserving homogeneous maps on the standard positive cone. The main goal of this paper is to…
Node-ranking methods that focus on structural importance are widely used in a variety of applications, from ranking webpages in search engines to identifying key molecules in biomolecular networks. In real social, supply chain, and…
Finding pertinent information is not limited to search engines. Online communities can amplify the influence of a small number of power users for the benefit of all other users. Users' information foraging in depth and breadth can be…
PageRank is a fundamental link analysis algorithm that also functions as a key representative of the performance of Sparse Matrix-Vector (SpMV) multiplication. The traditional PageRank implementation generates fine granularity random memory…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
In this paper we present a new method that can accelerate the computation of the PageRank importance vector. Our method, called D-Iteration (DI), is based on the decomposition of the matrix-vector product that can be seen as a fluid…
In web search, typically a candidate generation step selects a small set of documents---from collections containing as many as billions of web pages---that are subsequently ranked and pruned before being presented to the user. In Bing, the…
The rise of big data systems has created a need for benchmarks to measure and compare the capabilities of these systems. Big data benchmarks present unique scalability challenges. The supercomputing community has wrestled with these…
In network science, there is often the need to sort the graph nodes. While the sorting strategy may be different, in general sorting is performed by exploiting the network structure. In particular, the metric PageRank has been used in the…
Scientific recommender systems, such as Google Scholar and Web of Science, are essential tools for discovery. Search algorithms that power work through stigmergy, a collective intelligence mechanism that surfaces useful paths through…
How to rank web pages, scientists and online resources has recently attracted increasing attention from both physicists and computer scientists. In this paper, we study the ranking problem of rating systems where users vote objects by…
Ranking algorithms in traditional search engines are powered by enormous training data sets that are meticulously engineered and curated by a centralized entity. Decentralized peer-to-peer (p2p) networks such as torrenting applications and…