Tree Contractions and Evolutionary Trees

An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of species. An agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees. We give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees T_1 and T_2 with n leaves each. If the maximum degree d of these trees is bounded by a constant, the time complexity is O(n log^2(n)) and is within a log(n) factor of optimal. For general d, this algorithm runs in O(n d^2 log(d) log^2(n)) time or alternatively in O(n d sqrt(d) log^3(n)) time

Composing Distributed Data-intensive Web Services Using a Flexible Memetic Algorithm

Web Service Composition (WSC) is a particularly promising application of Web services, where multiple individual services with specific functionalities are composed to accomplish a more complex task, which must fulfil functional requirements and optimise Quality of Service (QoS) attributes, simultaneously. Additionally, large quantities of data, produced by technological advances, need to be exchanged between services. Data-intensive Web services, which manipulate and deal with those data, are of great interest to implement data-intensive processes, such as distributed Data-intensive Web Service Composition (DWSC). Researchers have proposed Evolutionary Computing (EC) fully-automated WSC techniques that meet all the above factors. Some of these works employed Memetic Algorithms (MAs) to enhance the performance of EC through increasing its exploitation ability of in searching neighbourhood area of a solution. However, those works are not efficient or effective. This paper proposes an MA-based approach to solving the problem of distributed DWSC in an effective and efficient manner. In particular, we develop an MA that hybridises EC with a flexible local search technique incorporating distance of services. An evaluation using benchmark datasets is carried out, comparing existing state-of-the-art methods. Results show that our proposed method has the highest quality and an acceptable execution time overall.Comment: arXiv admin note: text overlap with arXiv:1901.0556

Exact Asymptotic Results for a Model of Sequence Alignment

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the large c limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.Comment: 4 pages Revtex, 2 .eps figures include

Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment

For the Bernoulli Matching model of sequence alignment problem we apply the Bethe ansatz technique via an exact mapping to the 5--vertex model on a square lattice. Considering the terrace--like representation of the sequence alignment problem, we reproduce by the Bethe ansatz the results for the averaged length of the Longest Common Subsequence in Bernoulli approximation. In addition, we compute the average number of nucleation centers of the terraces.Comment: 14 pages, 5 figures (some points are clarified