Related papers: Enumeration of sequences with large alphabets
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…
The advent of large language models (LLMs) has significantly advanced artificial intelligence (AI) in software engineering (SE), with source code embeddings playing a crucial role in tasks such as source code clone detection and source code…
Minimizers are sampling schemes with numerous applications in computational biology. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a linear order $\rho$ on strings of length $k$ (also…
An {\em ancestry labeling scheme} labels the nodes of any tree in such a way that ancestry queries between any two nodes in a tree can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of…
In this paper, we present an involution on some kind of colored $k$-ary trees which provides a combinatorial proof of a combinatorial sum involving the generalized Catalan numbers $C_{k,\gamma}(n)=\frac{\gamma}{k n+\gamma}{k n+\gamma\choose…
Large-scale source-code clone detection is a challenging task. In our previous work, we proposed an approach (SSCD) that leverages artificial neural networks and approximates nearest neighbour search to effectively and efficiently locate…
We study the following combinatorial version of the Slepian-Wolf coding scheme. Two isolated Senders are given binary strings $X$ and $Y$ respectively; the length of each string is equal to $n$, and the Hamming distance between the strings…
We extend the notion of an enumeration scheme developed by Zeilberger and Vatter to the case of vincular patterns (also called "generalized patterns" or "dashed patterns"). In particular we provide an algorithm which takes in as input a set…
We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $\sigma \in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $\sigma$ is the size of the alphabet and…
This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar…
Large language models (LLMs) are increasingly used for semantic query processing over large corpora. A set of semantic operators derived from relational algebra has been proposed to provide a unified interface for expressing such queries,…
We present adaptive on-line schemes for lossy encoding of individual sequences under the conditions of the Wyner-Ziv (WZ) problem. In the first part of this article, a set of fixed-rate scalar source codes with zero delay is presented. We…
The $k$-mappability problem has two integers parameters $m$ and $k$. For every subword of size $m$ in a text $S$, we wish to report the number of indices in $S$ in which the word occurs with at most $k$ mismatches. The problem was lately…
Suppose Alice and Bob receive strings $X=(X_1,...,X_n)$ and $Y=(Y_1,...,Y_n)$ each uniformly random in $[s]^n$ but so that $X$ and $Y$ are correlated . For each symbol $i$, we have that $Y_i = X_i$ with probability $1-\eps$ and otherwise…
Given a dynamic set $K$ of $k$ strings of total length $n$ whose characters are drawn from an alphabet of size $\sigma$, a keyword dictionary is a data structure built on $K$ that provides locate, prefix search, and update operations on…
In this paper, we propose a source coding scheme that represents data from unknown distributions through frequency and support information. Existing encoding schemes often compress data by sacrificing computational efficiency or by assuming…
Embedding methods such as word embedding have become pillars for many applications containing discrete structures. Conventional embedding methods directly associate each symbol with a continuous embedding vector, which is equivalent to…