Abstract
Calculating the “distance” between two given objects with respect to a designated “editing” operation is a hot research area in bioinformatics, where the “distance” is always defined as the minimum number of the “editing” operations required to transform one object into the other one. One of the famous problems in the area is the Minimum Common String Partition problem, which is the simplified Minimum Tree Cut/Paste Distance problem. Within the paper, we consider another simplified version of the Minimum Tree Cut/Paste Distance problem, named Tree Assembly problem, of which the edge-deletion operations are specified. More specifically, the Tree Assembly problem aims to transform a given forest into a given tree by edge-addition operations only. In our investigations, we present a fixed-parameter algorithm with runtime \(2^{O(k \log k)} n^{O(1)}\) for the Tree Assembly problem, where k and n are the numbers of trees and nodes in the forest, respectively. Additionally, we give a polynomial-time algorithm for a restricted variant of the problem.
This work is supported by the National Natural Science Foundation of China under Grants 61802441, 61672536, 61420106009, 61872450.
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Shi, F., You, J., Zhang, Z., Liu, J. (2020). Tractabilities for Tree Assembly Problems. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_26
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