Related papers: On the work of dynamic constant-time parallel algo…
Tree data structures, such as red-black trees, quad trees, treaps, or tries, are fundamental tools in computer science. A classical problem in concurrency is to obtain expressive, efficient, and scalable versions of practical tree data…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…
We present the LATE algorithm, an asynchronous variant of the Earley algorithm for parsing context-free grammars. The Earley algorithm is naturally task-based, but is difficult to parallelize because of dependencies between the tasks. We…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Building models that take advantage of the hierarchical structure of language without a priori annotation is a longstanding goal in natural language processing. We introduce such a model for the task of machine translation, pairing a…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive…
With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…
Tree of Thoughts (ToT) enhances Large Language Model (LLM) reasoning by structuring problem-solving as a spanning tree. However, recent methods focus on search accuracy while overlooking computational efficiency. The challenges of…
The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without…
In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…
We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in $O(\log^4n/\log\log n)$ amortized time per operation, improving the $O(\log^4n)$ amortized bound of Holm et…
The problem of task scheduling with communication delays is strongly NP-hard. State-space search algorithms such as A* have been shown to be a promising approach to solving small to medium sized instances optimally. A recently proposed…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
We consider the dynamic range minimum problem on the ultra-wide word RAM model of computation. This model extends the classic $w$-bit word RAM model with special ultrawords of length $w^2$ bits that support standard arithmetic and boolean…
In this work we introduce a new linear time compression algorithm, called "Re-pair for Trees", which compresses ranked ordered trees using linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…
The dictionary matching is a task to find all occurrences of patterns in a set $D$ (called a dictionary) on a text $T$. The Aho-Corasick-automaton (AC-automaton) is a data structure which enables us to solve the dictionary matching problem…