A path recorder algorithm for Multiple Longest Common Subsequences (MLCS) problems

Motivation Searching the Longest Common Subsequences of many sequences is called a Multiple Longest Common Subsequence (MLCS) problem which is a very fundamental and challenging problem in many fields of data mining. The existing algorithms cannot be applicable to problems with long and large-scale sequences due to their huge time and space consumption. To efficiently handle large-scale MLCS problems, a Path Recorder Directed Acyclic Graph (PRDAG) model and a novel Path Recorder Algorithm (PRA) are proposed. Results In PRDAG, we transform the MLCS problem into searching the longest path from the Directed Acyclic Graph (DAG), where each longest path in DAG corresponds to an MLCS. To tackle the problem efficiently, we eliminate all redundant and repeated nodes during the construction of DAG, and for each node, we only maintain the longest paths from the source node to it but ignore all non-longest paths. As a result, the size of the DAG becomes very small, and the memory space and search time will be greatly saved. Empirical experiments have been performed on a standard benchmark set of both DNA sequences and protein sequences. The experimental results demonstrate that our model and algorithm outperform the related leading algorithms, especially for large-scale MLCS problems. Availability and implementation This program code is written by the first author and can be available at https://www.ncbi.nlm.nih.gov/nuccore and https://blog.csdn.net/wswguilin. Supplementary information Supplementary data are available at Bioinformatics online.

On the rate of convergence for the length of the longest common subsequences in hidden Markov models

Let (X, Y) = (Xn, Yn)n≥1 be the output process generated by a hidden chain Z = (Zn)n≥1, where Z is a finite-state, aperiodic, time homogeneous, and irreducible Markov chain. Let LCn be the length of the longest common subsequences of X1,..., Xn and Y1,..., Yn. Under a mixing hypothesis, a rate of convergence result is obtained for E[LCn]/n.

A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations

We address a question and a conjecture on the expected length of the longest common subsequences of two i.i.d. random permutations of $[n]:=\{1,2,...,n\}$. The question is resolved by showing that the minimal expectation is not attained in the uniform case. The conjecture asserts that $\sqrt{n}$ is a lower bound on this expectation, but we only obtain $\sqrt[3]{n}$ for it.

WiFi Fingerprint Localization for Emergency Response

As a key enabler for diversified location-based services (LBSs) of pervasive computing, indoor WiFi fingerprint localization remains a hot topic for decades. For most of previous research, maintaining a stable Radio Frequency (RF) environment constitutes one implicit but basic assumption. However, there is little room for such assumption in real-world scenarios, especially for the emergency response. Therefore, we propose a novel solution (HED) for rapidly setting up an indoor localization system by harvesting from the bursting number of available wireless resources. Via extensive real-world experiments lasting for over 6 months, we show the superiority of our HED algorithm in terms of accuracy, complexity and stability over two state-of-the-art solutions that are also designed to resist the dynamics, i.e., FreeLoc and LCS (Longest Common Subsequences). Moreover, experimental results not only confirm the benefits brought by environmental dynamics, but also provide valuable investigations and hand-on experiences on the real-world localization system.