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Motivated by the design of cost-efficient communication networks, the problem about Maximum Internal Spanning Tree that arises in a connected graph, is proposed to find a spanning tree with the maximum number of internal vertices. In 2018, Xingfu Li et al. presented a polynomial algorithm to find a maximum internal spanning tree in a connected interval graph. Based on the structure of normal orderings on interval graphs, we present a simple linear time algorithm that solve the problem when restricted to connected interval graphs in this paper. The proof provides additional insight about the linear time algorithm on interval graphs. • The MIST problem is solvable in a simple linear time algorithm under the restriction of connected interval graphs. • The structure of normal orderings on interval graphs is proposed to solve the Maximum Internal Spanning Tree problem. • The proof of the main results is more easy to understand with proper cases to prove. [ABSTRACT FROM AUTHOR]

The longest common palindromic subsequence (LCPS) problem is a variant of the longest common subsequence (LCS) problem. Given two input sequences A and B , the LCPS problem is to find the common subsequence of A and B such that the answer is a palindrome with the maximal length. The LCPS problem was first proposed by Chowdhury et al. (2014) [9] , who proposed a dynamic programming algorithm with O (m 2 n 2) time, where m and n denote the lengths of A and B , respectively. This paper proposes a diagonal-based algorithm for solving the LCPS problem with O (L (m − L) R log ⁡ n) time and O (R L) space, where R denotes the number of match pairs between A and B , and L denotes the LCPS length. In our algorithm, the 3-dimensional minima finding algorithm is invoked to overcome the domination problem. As experimental results show, our algorithm is efficient practically compared with some previously published algorithms. [ABSTRACT FROM AUTHOR]