Related papers: Deposition and Extension Approach to Find Longest …

A heapable sequence is a sequence of numbers that can be arranged in a "min-heap data structure". Finding a longest heapable subsequence of a given sequence was proposed by Byers, Heeringa, Mitzenmacher, and Zervas (ANALCO 2011) as a…

In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let $X$ and $Y$ be two strings over an alphabet $\Sigma$. The longest common subsequence and substring problem for $X$ and $Y$ is to…

Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…

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…

Knowledge-intensive multi-hop question answering (QA) tasks, which require integrating evidence from multiple sources to address complex queries, often necessitate multiple rounds of retrieval and iterative generation by large language…

In the area of Pattern Recognition and Matching, finding a Longest Common Subsequence plays an important role. In this paper, we have proposed one algorithm based on parallel computation. We have used OpenMP API package as middleware to…

We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…

Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…

Efficient long-sequence generation is a critical challenge for Large Language Models. While recent sparse decoding methods improve efficiency, they suffer from KV cache misalignment, where approximation errors accumulate and degrade…

The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes…

A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism…

The Longest Common Increasing Subsequence (LCIS) is a variant of the classical Longest Common Subsequence (LCS), in which we additionally require the common subsequence to be strictly increasing. While the well-known "Four Russians"…

Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…

Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off…

Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a…

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…

Modern trends in data collection are bringing current mainstream techniques for database query processing to their limits. Consequently, various novel approaches for efficient query processing are being actively studied. One such approach…