An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ excluding each of constrain string in $P$ as a substring and the length of $Z$ is maximized. The problem was declared to be NP-hard\cite{1}, but we finally found that this is not true. A new dynamic programming solution for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(nmr)$.Comment: arXiv admin note: substantial text overlap with arXiv:1301.718

A note on the largest number of red nodes in red-black trees

In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$ keys. Then the algorithm is improved to some $O(\log n)$ time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of $r(n)$

Complete Solutions for a Combinatorial Puzzle in Linear Time

In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n + m$. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of $n$ black checkers and $m$ white checkers, and finally, we present an explicit solution for the general game

Using fractional order method to generalize strengthening generating operator buffer operator and weakening buffer operator

Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases

An Auto-Parallelizer for Distributed Computing in Haskell

One of the main challenges in distributed computing is building interfaces and APIs that allow programmers with limited background in distributed systems to write scalable, performant, and fault-tolerant applications on large clusters. In this demonstration, we designed and implemented a Haskell auto-parallelizer with a simple yet powerful interface by taking advantage of the default purity of Haskell functions. Finally, we benchmarked our implementation on a set of examples to illustrate the potential for future work in this direction.Comment: 2 pages excluding title page and reference page. 2 figures. This work was submitted to the 28th ACM SIGPLAN International Conference on Functional Programming, Haskell Symposium. This work was accepted for oral presentation and was presented on Sep 8, 202