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TR05-153 | 9th December 2005 00:00

Testing Orientation Properties


Authors: Shirley Halevy, Oded Lachish, Ilan Newman, Dekel Tsur
Publication: 12th December 2005 10:07
Downloads: 2692


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.

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