Algorithms for solving the symmetry number problem on trees

Authors:
Pradipta Prometheus Mitra;Muhammad Arshad Ul Abedin;Md. Abul Kashem
Affiliations:
Yale University, New Haven, CT;Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh;Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
Venue:
Information Processing Letters
Year:
2004

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Abstract

The symmetry number of a tree is defined as the number of nodes of the maximum subtree of the tree that exhibits axial symmetry. Chin and Yen have presented an algorithm for solving the problem of finding the symmetry number of unrooted unordered trees in time O(n4). In this paper we present an improved algorithm for solving the symmetry number problem on trees that runs in time O(n3). We also show that our algorithm needs O(n2 log n) time for trees with bounded degrees.