COLT '90 Proceedings of the third annual workshop on Computational learning theory
Confluent and Other Types of Thue Systems
Journal of the ACM (JACM)
Inferring the structure of a Markov Chain from its output
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Inferring a graph from path frequency
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Inferring a graph from path frequency
Discrete Applied Mathematics
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Aslam and Rivest considered the problem of inferring the smallest edge-colored graph of degree bound k consistent with the sequence of colors seen in a walk of the graph. Using Church-Rosser properties of certain sets of rewrite rules, they gave a polynomial time algorithm for the case of k = 2. The straightforward implementation of their ideas results in an O(n^5) algorithm, where n is the length of the walk. In this paper, we develop their ideas further and give an O(n log n) algorithm for the same problem. We also show that if the degree bound k is greater than two, then the decision version of the problem is NP-complete, thus settling a conjecture of Aslam and Rivest.