A faster fixed-parameter algorithm for computing an optimal alignment for bounded degree trees

JSAI Technical Report, SIG-FPAI  
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
more » ... , 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.
doi:10.11517/jsaifpai.108.0_07 fatcat:lf6zgs3qs5bszks3qldd5mprpe