Completely Described Undirected Graph Structure

Marginalizing in Undirected Graph and Hypergraph Models

Given an undirected graph g or hypergraph 'H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph YA or hy­ pergraph 'HA associated with a given subset A c V such that the marginal distribution of A factorizes according to YA or 'HA, respec­ tively. Finally, we illustrate the method by its application to some practical examples. Wi...

Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata

We investigate time-space tradeoffs for traversing undirected graphs, using a variety of structured models that are all variants of Cook and Rackoff's ``Jumping Automata for Graphs.'' Our strongest tradeoff is a quadratic lower bound on the product of time and space for graph traversal. For example, achieving linear time requires linear space, implying that depth-first search is optimal. Since ...

Parallel Strong Orientation of an Undirected Graph

Time-Space Tradeoffs for Undirected Graph Traversal

We prove time-space tradeoffs for traversing undirected graphs. One of these is a quadratic lower bound on a deterministic model that closely matches the recent probabilistic upper bound of Broder, Karlin, Raghavan, and Upfal. The models used are variants of Cook and Rackoff’s “Jumping Automata for Graphs”. 1 The Complexity of Graph Traversal Graph traversal is a fundamental problem in computin...

Structural controllability: an undirected graph approach

This paper addresses questions regarding controllability for ‘generic parameter’ dynamical systems, i.e. the question whether a dynamical system is ‘structurally controllable’. Unlike conventional methods that deal with structural controllability, our approach uses an undirected graph: the behavioral approach to modelling dynamical systems allows this. Given a system of linear, constant coeffic...