Succinct Preferential Attachment Graphs

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Alaoui, Ziad Ismaili, Namrata, Wild, Sebastian
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866911024626532352
author Alaoui, Ziad Ismaili
Namrata
Wild, Sebastian
author_facet Alaoui, Ziad Ismaili
Namrata
Wild, Sebastian
contents Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully generalised to trees. For graphs, support for computing over compressed data remains patchy; typical results in the area of succinct data structures are restricted to a specific class of graphs and use the same, worst-case amount of space for any graph from this class. In this work, we design a data structure whose space usage automatically improves with the compressibility of the graph at hand, while efficiently supporting navigational operations (simulating adjacency-list access). Specifically, we show that the space usage approaches the instance-optimal space when the graph is drawn according to the classic Barabási-Albert model of preferential-attachment graphs. Our data-structure techniques also work for arbitrary graphs, guaranteeing a size asymptotically no larger than an entropy-compressed edge list. A key technical contribution is the careful analysis of the instance-optimal space usage.
format Preprint
id arxiv_https___arxiv_org_abs_2506_21436
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Succinct Preferential Attachment Graphs
Alaoui, Ziad Ismaili
Namrata
Wild, Sebastian
Data Structures and Algorithms
Information Theory
Probability
Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully generalised to trees. For graphs, support for computing over compressed data remains patchy; typical results in the area of succinct data structures are restricted to a specific class of graphs and use the same, worst-case amount of space for any graph from this class. In this work, we design a data structure whose space usage automatically improves with the compressibility of the graph at hand, while efficiently supporting navigational operations (simulating adjacency-list access). Specifically, we show that the space usage approaches the instance-optimal space when the graph is drawn according to the classic Barabási-Albert model of preferential-attachment graphs. Our data-structure techniques also work for arbitrary graphs, guaranteeing a size asymptotically no larger than an entropy-compressed edge list. A key technical contribution is the careful analysis of the instance-optimal space usage.
title Succinct Preferential Attachment Graphs
topic Data Structures and Algorithms
Information Theory
Probability
url https://arxiv.org/abs/2506.21436