Improved Algorithm for the Symmetry Number Problem on Trees
نویسنده
چکیده
The symmetry number of a tree is defined as the number of nodes of the maximum subtree of the tree that exhibits axial symmetry. The best previous algorithm for computing the symmetry number for an unrooted unordered tree is due to Mitra et al. [8] and runs in O(n) time. In this paper we show an improvement on this time complexity by encoding small trees. Our algorithm runs in time O(n(log logn/ logn)).
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For trees, we define the notion of the so-called symmetry number to measure the size of the maximum subtree that exhibits an axial symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a polynomial time algorithm for computing the symmetry number. 2001 Elsevier Science B.V. All rights reserved.
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