TR05-153 Authors: Shirley Halevy, Oded Lachish, Ilan Newman, Dekel Tsur

Publication: 12th December 2005 10:07

Downloads: 1828

Keywords:

We propose a new model for studying graph related problems

that we call the \emph{orientation model}. In this model, an undirected

graph $G$ is fixed, and the input is any possible edge orientation

of $G$. A property is now a property of the directed graph that is

obtained by a given orientation. The distance between two

orientations is the number of edges that have to be redirected in

order to move from one digraph to the other.

This model allows studying digraph properties such as not containing a

forbidden (induced) subgraph, being strongly connected etc., for

every underlying graph including sparse graphs. As it turns out,

this model generalizes the standard, adjacency matrix

model. That is, we show that for every graph property $\mathcal{P}$

of dense graphs

there is a property of

orientations that is testable if and only if $\mathcal{P}$ is.

This model is also handy in some practical

situations of networks, in which the underlying network is fixed

while the direction of (weighted) links may vary.

We show that several orientations properties are testable in this

model (for every underlying graph),

while some are not.