Estimating graph parameters with random walks

Estimating graph parameters via random walks with restarts

In this paper we discuss the problem of estimating graph parameters from a random walk with restarts. In this setting, an algorithm observes the trajectory of a random walk over an unknown graph G, starting from a vertex x. The algorithm also sees the degrees along the trajectory. The only other power that the algorithm has is to request that the random walk be reset to its initial state x at a...

Estimating Graph Parameters from Random Order Streams

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with probability at least 2/3, • the number of connected components of G can be approximated up to an additive error of εn using (1ε ) O(1/ε) space, • the weight o...

Lexical Semantic Relatedness with Random Graph Walks

Many systems for tasks such as question answering, multi-document summarization, and information retrieval need robust numerical measures of lexical relatedness. Standard thesaurus-based measures of word pair similarity are based on only a single path between those words in the thesaurus graph. By contrast, we propose a new model of lexical semantic relatedness that incorporates information fro...

Random Walks and Graph Homomorphisms

Graph homomorphisms through random walks

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff– Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which...