相关论文: Linear Time Online Algorithms for Constructing Lin…

A \emph{tree cut-sparsifier} $T$ of quality $\alpha$ of a graph $G$ is a single tree that preserves the capacities of all cuts in the graph up to a factor of $\alpha$. A \emph{tree flow-sparsifier} $T$ of quality $\alpha$ guarantees that…

Standard subword tokenization methods fragment numbers inconsistently, causing large language models (LLMs) to lose positional and decimal structure - a primary driver of errors in arithmetic and scientific reasoning. We introduce Triadic…

We propose a B tree representation storing $n$ keys, each of $k$ bits, in either (a) $nk + O(nk / \lg n)$ bits or (b) $nk + O(nk \lg \lg n/ \lg n)$ bits of space supporting all B tree operations in either (a) $O(\lg n )$ time or (b) $O(\lg…

Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…

In this paper we generalize the definition of "Search Trees" (ST) to enable reference values other than the key of prior inserted nodes. The idea builds on the assumption an $n$-node AVL (or Red-Black) requires to assure $O(\log_2n)$…

The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…

The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…

We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al.…

Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of $n$ keys from a totally ordered universe in this context. We introduce a two-layer data…

Given a string $T$ of length $n$ over an alphabet $\Sigma\subset \{1,2,\ldots,n^{O(1)}\}$ of size $\sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $\Sigma$ that is…

A run in a string is a maximal periodic substring. For example, the string $\texttt{bananatree}$ contains the runs $\texttt{anana} = (\texttt{an})^{3/2}$ and $\texttt{ee} = \texttt{e}^2$. There are less than $n$ runs in any length-$n$…

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…

The suffix array, perhaps the most important data structure in modern string processing, is often augmented with the longest common prefix (LCP) array which stores the lengths of the LCPs for lexicographically adjacent suffixes of a string.…

In almost all text generation applications, word sequences are constructed in a left-to-right (L2R) or right-to-left (R2L) manner, as natural language sentences are written either L2R or R2L. However, we find that the natural language…

An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their…

Given a string $T$ with length $n$ whose characters are drawn from an ordered alphabet of size $\sigma$, its longest Lyndon subsequence is a longest subsequence of $T$ that is a Lyndon word. We propose algorithms for finding such a…

In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…

Let $\Sigma$ and $\Pi$ be disjoint alphabets of respective size $\sigma$ and $\pi$. Two strings over $\Sigma \cup \Pi$ of equal length are said to parameterized match (p-match) if there is a bijection $f:\Sigma \cup \Pi \rightarrow \Sigma…

We show that the number of distinct squares in a packed string of length $n$ over an alphabet of size $\sigma$ can be computed in $O(n/\log_\sigma n)$ time in the word-RAM model. This paper is the first to introduce a sublinear-time…

Suffix trees have recently become very successful data structures in handling large data sequences such as DNA or Protein sequences. Consequently parallel architectures have become ubiquitous. We present a novel alphabet-dependent parallel…