ﻻ يوجد ملخص باللغة العربية
The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to support efficient on-line pattern queries. We study this problem in the case where the text is weighted: for every position of the text and every letter of the alphabet a probability of occurrence of this letter at this position is given. Sequences of this type, also called position weight matrices, are commonly used to represent imprecise or uncertain data. A weighted sequence may represent many different strings, each with probability of occurrence equal to the product of probabilities of its letters at subsequent positions. Given a probability threshold $1/z$, we say that a pattern string $P$ matches a weighted text at position $i$ if the product of probabilities of the letters of $P$ at positions $i,ldots,i+|P|-1$ in the text is at least $1/z$. In this article, we present an $O(nz)$-time construction of an $O(nz)$-sized index that can answer pattern matching queries in a weighted text in optimal time improving upon the state of the art by a factor of $z log z$. Other applications of this data structure include an $O(nz)$-time construction of the weighted prefix table and an $O(nz)$-time computation of all covers of a weighted sequence, which improve upon the state of the art by the same factor.
Weighted Szeged index is a recently introduced extension of the well-known Szeged index. In this paper, we present a new tool to analyze and characterize minimum weighted Szeged index trees. We exhibit the best trees with up to 81 vertices and use th
Understanding the correlation between two different scores for the same set of items is a common problem in information retrieval, and the most commonly used statistics that quantifies this correlation is Kendalls $tau$. However, the standard definit
We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(log P)$-competitive algorithm, where $P$ is the maximum-to-minimum p
In this paper, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA 2020) on
Sequences set is a mathematical model used in many applications. As the number of the sequences becomes larger, single sequence set model is not appropriate for the rapidly increasing problem sizes. For example, more and more text processing applicat