Tree alignment is known as one of similarity measures between rooted trees. The problem of computing an optimal alignment is known to be not only NP-hard but also MAX SNP-hard for unordered trees, whereas it is solvable in polynomial time for ordered counterpart. Jiang et al. (TCS, 1995) gave a fast algorithm for unordered trees with bounded degree, which runs in O(6 ∆ ∆nm) time, where n and m are the number of vertices of the input trees and ∆ is the maximum degree of those trees. In this

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... , we improve the exponential part in the running time 6 ∆ to 4 ∆ , with a sacrifice of the polynomial dependency in the running time, by means of the well-known fast subset convolution technique. We also show that it seems unlikely to exist any drastic improvement of the running time: Under the Exponential Time Hypothesis (ETH), there is no 2 o(∆) (n + m) O(1) time algorithm for computing an optimal alignment between unordered trees. In order to evaluate the practical performance of the proposed algorithm, we have conducted a computational experiment.