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In this paper, we first define the longest almost increasing subsequence with sliding windows (LaISW), a generalization that combines the longest increasing subsequence with sliding windows (LISW) problem and the longest almost increasing subsequence (LaIS) problem. For a numeric sequence A , a window size w and a tolerance constant c , the goal of the LaISW problem is to identify the LaIS within all windows of size w in A. In an almost increasing subsequence, slight decreases smaller than c are permitted. We propose an efficient algorithm for solving the LaISW problem. Instead of constructing the entire row tower, our algorithm computes the change in drop out (occurrence) for each element in the row tower. The time complexity of our algorithm is O (n L) , and the space complexity is O(L), where n and L represent the lengths of the input sequence and the LaISW answer, respectively. • Stock prices might exhibit an almost increasing (or decreasing) trend, but they are not strictly increasing. • We define longest almost increasing subsequence with sliding windows (LaISW). • Our algorithm calculates the changes in occurrences for each element in the row tower. • The time and space complexities of our algorithm are O (n L) and O(L), respectively. [ABSTRACT FROM AUTHOR]

The hypercube is a very popular topology for the interconnection networks of parallel systems, and the folded hypercube is a variant of the hypercube. The folded hypercube attains much higher performance by introducing one additional link to each processing element. Therefore, there are many research activities regarding the folded hypercube. We focus on this topology and address an unresolved problem, that is, the set-to-set disjoint paths problem in it. In this paper, we show an algorithm that solves the problem in a folded hypercube in polynomial time. We prove the correctness of the algorithm. Moreover, we show that the time complexity of the algorithm is O (ν 3 log ⁡ ν) and the maximum length of the paths is 2 ν + 2 if the algorithm is applied to a ν -dimensional folded hypercube. • This study proposes an algorithm that solves the set-to-set disjoint paths problem in a folded hypercube in polynomial time. • (v + 1) paths are generated between two node sets, each of which has (v + 1) nodes, in a v -dimensional folded hypercube. • It is proved that the proposed algorithm solves the problem in a v -dimensional folded hypercube in O (v 3 log ⁡ v) time. • Also, it is proved that the lengths of the paths generated by the proposed algorithm are at most 2 v + 2. [ABSTRACT FROM AUTHOR]

Reconstructing input from a data structure entails determining whether an instance of the data structure is in fact valid or not, and if valid, discovering the underlying data that it represents. In this paper we consider the parameterized suffix array (pSA) along with its corresponding parameterized longest-common-prefix (pLCP) array and solve the following problem. Given two arrays of numbers as input, A and P , does there exist a parameterized string S such that A is its pSA and P is its pLCP array? If the answer is positive, our algorithm produces a string S whose pSA is A and whose pLCP array is P. Although the naive approach would have to consider an exponential number of possibilities for such a string S , our algorithm's time complexity is only O (n 2) for input arrays of size n. [ABSTRACT FROM AUTHOR]