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Inferring Graphs from Walks (Extended Abstract)

Summary: Inferring Graphs from Walks
(Extended Abstract)
Javed A. Aslam # Ronald L. Rivest +
Laboratory for Computer Science
Massachusetts Institute of Technology
Cambridge, MA 02139
We consider the problem of inferring an undirected, degree­bounded, edge­colored
graph from the sequence of edge colors seen in a walk of that graph. This problem can
be viewed as reconstructing the structure of a Markov chain from its output. (That is,
we are not concerned with inferring the transition probabilities, but only the underlying
graph structure of the Markov chain.) We present polynomial­time algorithms for the
inference of underlying graphs of degree­bound 2 (linear chains and cycles), based on
some surprising properties about the confluence of various sets of rewrite rules.
1 Introduction
Consider an undirected, edge­colored graph G = (V, E, c) with vertex set V , edge set E,
and edge coloring c : E ## #. A walk of G starts at some vertex v i and makes transitions
from vertex to vertex by arbitrarily selecting some edge incident on the current vertex and
traversing it. The output of such a walk is the sequence of colors of the edges traversed.
We ask: given the output of a walk and a degree­bound k, what is the smallest undirected,


Source: Aslam, Javed - College of Computer Science, Northeastern University


Collections: Computer Technologies and Information Sciences