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The linear search problem, informally known as the cow path problem, is one of the fundamental problems in search theory. In this problem, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher,…
In models using pair-wise (ratio) comparisons among alternatives, a cardinal ranking vector should be deduced from a reciprocal matrix. The right Perron eigenvector (RP) was traditionally used, though several other options have emerged. We…
In this paper we study a property of time-dependent graphs, dubbed path ranking invariance. Broadly speaking, a time-dependent graph is path ranking invariant if the ordering of its paths (w.r.t. travel time) is independent of the start…
We introduce a new framework for web page ranking -- reinforcement ranking -- that improves the stability and accuracy of Page Rank while eliminating the need for computing the stationary distribution of random walks. Instead of relying on…
Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating…
A fundamental problem arising in many applications in Web science and social network analysis is, given an arbitrary approximation factor $c>1$, to output a set $S$ of nodes that with high probability contains all nodes of PageRank at least…
We present a new method to accelerate the HITS algorithm by exploiting hyperlink structure of the web graph. The proposed algorithm extends the idea of authority and hub scores from HITS by introducing two diagonal matrices which contain…
In this paper we have modified the existing page ranking mechanism as an advanced Page Rank Algorithm based on Semantics Inlinks Outlinks and Google Analytics. We have used Semantics page ranking to rank pages according to the word searched…
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…
Ranking is at the core of Information Retrieval. Classic ranking optimization studies often treat ranking as a sorting problem with the assumption that the best performance of ranking would be achieved if we rank items according to their…
The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…
PageRank is a widespread model for analysing the relative relevance of nodes within large graphs arising in several applications. In the current paper, we present a cost-effective Hessenberg-type method built upon the Hessenberg process for…
A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a…
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
We present an efficient algorithm for solving local linear systems with a boundary condition using the Green's function of a connected induced subgraph related to the system. We introduce the method of using the Dirichlet heat kernel…
The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at…
To rank nodes in quasi-hierarchical networks of social nature, it is necessary to carry out a detailed analysis of the network and evaluate the results obtained according to all the given criteria and identify the most influential nodes.…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
Recently, Tensor Ring Networks (TRNs) have been applied in deep networks, achieving remarkable successes in compression ratio and accuracy. Although highly related to the performance of TRNs, rank selection is seldom studied in previous…