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In this work, we present a new iterative exact solution algorithm for the weighted fair sequences problem, which is a recently introduced NP-hard sequencing problem with applications in diverse areas such as TV advertisement scheduling,…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
Given two strings $S$ and $P$, the Episode Matching problem is to find the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997) , where $n,m$ are…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
The Longest Common Subsequence (LCS) of two strings is a fundamental string similarity measure with a classical dynamic programming solution taking quadratic time. Despite significant efforts, little progress was made in improving the…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
Consider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target…
Calculating the length of a longest common subsequence (LCS) of two strings $A$ and $B$ of length $n$ and $m$ is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation…
Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the…
When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a…
The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
This work is devoted to solving some closely related open problems on the average and asymptotic behavior of the $2$-adic complexity of binary sequences. First, for fixed $N$, we prove that the expected value $E^{\mathrm{2-adic}}_N$ of the…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…