An algebraic approach to the prefix model analysis of binary trie structures and set intersection algorithms

AbstractThe trie, or digital tree, is a standard data structure for representing sets of strings over a given finite alphabet. Since Knuth's original work (1973), these data structures have been extensively studied and analyzed. In this paper, we present an algebraic approach to the analysis of average storage and average time required by the retrieval algorithms of trie structures under the prefix model. This approach extends the work of Flajolet et al. for other models which, unlike the prefix model, assume that no key in a sample set is the prefix of another. As the main application, we analyze the average running time of two algorithms for computing set intersections

Advanced rank/select data structures: succinctness, bounds and applications.

The thesis explores new theoretical results and applications of rank and select data structures. Given a string, select(c, i) gives the position of the ith occurrence of character c in the string, while rank(c, p) counts the number of instances of character c on the left of position p. Succinct rank/select data structures are space-efficient versions of standard ones, designed to keep data compressed and at the same time answer to queries rapidly. They are at the basis of more involved compressed and succinct data structures which in turn are motivated by the nowadays need to analyze and operate on massive data sets quickly, where space efficiency is crucial. The thesis builds up on the state of the art left by years of study and produces results on multiple fronts. Analyzing binary succinct data structures and their link with predecessor data structures, we integrate data structures for the latter problem in the former. The result is a data structure which outperforms the one of Patrascu 08 in a range of cases which were not studied before, namely when the lower bound for predecessor do not apply and constant-time rank is not feasible. Further, we propose the first lower bound for succinct data structures on generic strings, achieving a linear trade-off between time for rank/select execution and additional space (w.r.t. to the plain data) needed by the data structure. The proposal addresses systematic data structures, namely those that only access the underlying string through ADT calls and do not encode it directly. Also, we propose a matching upper bound that proves the tightness of our lower bound. Finally, we apply rank/select data structures to the substring counting problem, where we seek to preprocess a text and generate a summary data structure which is stored in lieu of the text and answers to substring counting queries with additive error. The results include a theory-proven optimal data structure with generic additive error and a data structure that errs only on infrequent patterns with significative practical space gains

Inquiries into words, constraints and contexts : Festschrift in the honour of Kimmo Koskenniemi on his 60th birthday

Peer reviewe

A Beginner\u27s Guide to Scala, Object Orientation and Functional Programming

Scala is now an established programming language developed by Martin Oderskey and his team at the EPFL. The name Scala is derived from Sca(lable) La(nguage). Scala is a multi-paradigm language, incorporating object oriented approaches with functional programming. Although some familiarity with standard computing concepts is assumed (such as the idea of compiling a program and executing this compiled from etc.) and with basic procedural language concepts (such as variables and allocation of values to these variables) the early chapters of the book do not assume any familiarity with object orientation nor with functional programming These chapters also step through other concepts with which the reader may not be familiar (such as list processing). From this background, the book provides a practical introduction to both object and functional approaches using Scala. These concepts are introduced through practical experience taking the reader beyond the level of the language syntax to the philosophy and practice of object oriented development and functional programming. Students and those actively involved in the software industry will find this comprehensive introduction to Scala invaluable

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems