Related papers: De Dictionariis Dynamicis Pauco Spatio Utentibus
In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…
We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be…
The proof that Large Language Models (LLMs) augmented with external read-write memory constitute a computationally universal system has established the theoretical foundation for general-purpose agents. However, existing implementations…
Sentiment analysis has become increasingly important for assessing public opinion and informing decision-making. Large language models (LLMs) have revolutionized this field by capturing nuanced language patterns. However, adapting LLMs to…
We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on $n$ vertices up to a $1+\epsilon$ error must…
Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, we extend the analysis of the orthogonal greedy algorithm…
We study a generalization of the classic paging problem that allows the amount of available memory to vary over time - capturing a fundamental property of many modern computing realities, from cloud computing to multi-core and…
We investigate the behaviour space of meta-heuristic optimisation algorithms automatically generated by Large Language Model driven algorithm discovery methods. Using the Large Language Evolutionary Algorithm (LLaMEA) framework with a GPT…
Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an…
We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…
We design a space-efficient algorithm for performing depth-first search traversal(DFS) of a graph in $O(m+n\log^* n)$ time using $O(n)$ bits of space. While a normal DFS algorithm results in a DFS-tree (in case the graph is connected), our…
We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…
The problem of fast items retrieval from a fixed collection is often encountered in most computer science areas, from operating system components to databases and user interfaces. We present an approach based on hash tables that focuses on…
Ternary weight quantization (e.g., BitNet b1.58) offers a promising path to mitigate the memory bandwidth bottleneck in Large Language Model (LLM) inference. However, conventional compute platforms lack native support for ternary-weight…
Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an…
We propose online algorithms for sequential learning in the contextual multi-armed bandit setting. Our approach is to partition the context space and then optimally combine all of the possible mappings between the partition regions and the…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
Let \((a_n)_{n \in \mathbb{N}}\) be a lacunary sequence of integers satisfying the Hadamard gap condition. For any fixed dimension $d \geq 1$, we establish asymptotic upper bounds for the maximal gap in the set of dilates…
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…
The access lemma (Sleator and Tarjan, JACM 1985) is a property of binary search trees that implies interesting consequences such as static optimality, static finger, and working set property. However, there are known corollaries of the…