From Theory to Practice: Plug and Play with Succinct Data Structures

Engineering efficient implementations of compact and succinct structures is a time-consuming and challenging task, since there is no standard library of easy-to- use, highly optimized, and composable components. One consequence is that measuring the practical impact of new theoretical proposals is a difficult task, since older base- line implementations may not rely on the same basic components, and reimplementing from scratch can be very time-consuming. In this paper we present a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements. We demonstrate the functionality of the framework by recomposing succinct solutions for document retrieval.Comment: 10 pages, 4 figures, 3 table

Succinct Data Structures for Chordal Graphs

We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time. We study the problem of succinctly storing a static chordal graph to answer adjacency, degree, neighbourhood and shortest path queries. Let G be a chordal graph with n vertices. We design a data structure using the information theoretic minimal n^2/4 + o(n^2) bits of space to support the queries: - whether two vertices u,v are adjacent in time f(n) for any f(n) in omega(1). - the degree of a vertex in O(1) time. - the vertices adjacent to u in (f(n))^2 time per neighbour - the length of the shortest path from u to v in O(nf(n)) tim

Proving Tree Algorithms for Succinct Data Structures

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely on cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect of two different tree-based succinct representations and their accompanying algorithms. One is the Level-Order Unary Degree Sequence, which encodes the structure of a tree in breadth-first order as a sequence of bits, where access operations can be defined in terms of Rank and Select, which work in constant time for static bit sequences. The other represents dynamic bit sequences as binary balanced trees, where Rank and Select present a low logarithmic overhead compared to their static versions, and with efficient insertion and deletion. The two can be stacked to provide a dynamic representation of dictionaries for instance. While both representations are well-known, we believe this to be their first formalization and a needed step towards provably-safe implementations of big data

Succinct Data Structures in the Realm of GIS

Presented at the 4th XoveTIC Conference, A Coruña, Spain, 7–8 October 2021.[Abstract] Geographic Information Systems (GIS) have spread all over our technological environment in the last decade. The inclusion of GPS technologies in everyday portable devices along with the creation of massive shareable geographical data banks has boosted the rise of geoinformatics. Despite the technological maturity of this field, there are still relevant research challenges concerning efficient information storage and representation. One of the most powerful techniques to tackle these issues is designing new Succinct Data Structures (SDS). These structures are defined by three main characteristics: they use a compact representation of the data, they have self-index properties and, as a consequence, they do not need decompression to process the enclosed information. Thus, SDS are not only capable of storing geographical data using as little space as possible, but they can also solve queries efficiently without any previous decompression. This work introduces how SDS can be successfully applied in the GIS context through several novel approaches and practical use cases.This work is partially funded by the CITIC research center funded by Xunta/FEDER-UE 2014-2020 Program, ED431G 2019/01. MICINN(PGE/ERDF) [EXTRA-Compact: PID2020-114635RB-I00]Xunta de Galicia; ED431G 2019/0

LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas, from data structures to algorithms: some compressed succinct indices for range minimum queries; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and indirect application in time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur