I/O efficient bisimulation partitioning on very large directed acyclic graphs

In this paper we introduce the first efficient external-memory algorithm to compute the bisimilarity equivalence classes of a directed acyclic graph (DAG). DAGs are commonly used to model data in a wide variety of practical applications, ranging from XML documents and data provenance models, to web taxonomies and scientific workflows. In the study of efficient reasoning over massive graphs, the notion of node bisimilarity plays a central role. For example, grouping together bisimilar nodes in an XML data set is the first step in many sophisticated approaches to building indexing data structures for efficient XPath query evaluation. To date, however, only internal-memory bisimulation algorithms have been investigated. As the size of real-world DAG data sets often exceeds available main memory, storage in external memory becomes necessary. Hence, there is a practical need for an efficient approach to computing bisimulation in external memory. Our general algorithm has a worst-case IO-complexity of O(Sort(|N| + |E|)), where |N| and |E| are the numbers of nodes and edges, resp., in the data graph and Sort(n) is the number of accesses to external memory needed to sort an input of size n. We also study specializations of this algorithm to common variations of bisimulation for tree-structured XML data sets. We empirically verify efficient performance of the algorithms on graphs and XML documents having billions of nodes and edges, and find that the algorithms can process such graphs efficiently even when very limited internal memory is available. The proposed algorithms are simple enough for practical implementation and use, and open the door for further study of external-memory bisimulation algorithms. To this end, the full open-source C++ implementation has been made freely available

LEDA-SM: External Memory Algorithms and Data Structures in theory and practice

Data to be processed has dramatically increased during the last years. Nowadays, external memory (mostly hard disks) has to be used to store this massive data. Algorithms and data structures that work on external memory have different properties and specialties that distinguish them from algorithms and data structures, developed for the RAM model. In this thesis, we first explain the functionality of external memory,which is realized by disk drives. We then introduce the most important theoretical I/O models. In the main part, we present the C++ class library LEDA-SM. Library LEDA-SM is an extension of the LEDA library towards external memory computation and consists of a collection of algorithms and data structures that are designed to work efficiently in external memory. In the last two chapters, we present new external memory data structures for external memory priority queues and new external memory construction algorithms for suffix arrays. These new proposals are theoretically analyzed and experimentally tested. All proposals are implemented using the LEDA-SM library. Their efficiency is evaluated by performing a large number of experiments.Die zu verarbeitenden Datenmengen sind in den letzten Jahren dramatisch gestiegen, so daß Externspeicher (in Form von Festplatten) eingesetzt wird, um die Datenmengen zu speichern. Algorithmen und Datenstrukturen, die den Externspeicher benutzen, haben andere algorithmische Anforderungen als eine Vielzahl der bekannten Algorithmen und Datenstrukturen, die für das RAM-Modell entwickelt wurden. Wir geben in dieser Arbeit erst einen Einblick in die Funktionsweise von Externspeicher anhand von Festplatten und erklären die wichtigsten theoretischen Modelle, die zur Analyse von Algorithmen benutzt werden. Weiterhin stellen wir eine neu entwickelte C++ Klassenbibliothek namens LEDA-SM vor. LEDA-SM bietet eine Sammlung von speziellen Externspeicher Algorithmen und Datenstrukturen. Im zweiten Teil entwickeln wir neue Externspeicher-Prioritätswarteschlangen und neue Externspeicher- Konstruktionsalgorithmen für Suffix Arrays. Unsere neuen Verfahren werden theoretisch analysiert, mit Hilfe von LEDA-SM implementiert und anschließend experimentell getestet

Characterizing the performance of Flash memory storage devices and its impact on algorithm design

Initially used in digital audio players, digital cameras, mobile phones, and USB memory sticks, flash memory may become the dominant form of end-user storage in mobile computing, either completely replacing the magnetic hard disks or being an additional secondary storage. We study the design of algorithms and data structures that can exploit the flash memory devices better. For this, we characterize the performance of NAND flash based storage devices, including many solid state disks. We show that these devices have better random read performance than hard disks, but much worse random write performance. We also analyze the effect of misalignments, aging and past I/O patterns etc. on the performance obtained on these devices. We show that despite the similarities between flash memory and RAM (fast random reads) and between flash disk and hard disk (both are block based devices), the algorithms designed in the RAM model or the external memory model do not realize the full potential of the flash memory devices. We later give some broad guidelines for designing algorithms which can exploit the comparative advantages of both a flash memory device and a hard disk, when used together

Lempel-Ziv Parsing in External Memory

For decades, computing the LZ factorization (or LZ77 parsing) of a string has been a requisite and computationally intensive step in many diverse applications, including text indexing and data compression. Many algorithms for LZ77 parsing have been discovered over the years; however, despite the increasing need to apply LZ77 to massive data sets, no algorithm to date scales to inputs that exceed the size of internal memory. In this paper we describe the first algorithm for computing the LZ77 parsing in external memory. Our algorithm is fast in practice and will allow the next generation of text indexes to be realised for massive strings and string collections.Comment: 10 page

Lightweight LCP Construction for Very Large Collections of Strings

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several applications, especially in biological contexts. Nowadays, the input data for many problems are big collections of strings, for instance the data coming from "next-generation" DNA sequencing (NGS) technologies. In this paper we present the first lightweight algorithm (called extLCP) for the simultaneous computation of the longest common prefix array and the Burrows-Wheeler transform of a very large collection of strings having any length. The computation is realized by performing disk data accesses only via sequential scans, and the total disk space usage never needs more than twice the output size, excluding the disk space required for the input. Moreover, extLCP allows to compute also the suffix array of the strings of the collection, without any other further data structure is needed. Finally, we test our algorithm on real data and compare our results with another tool capable to work in external memory on large collections of strings.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The final version of this manuscript is in press in Journal of Discrete Algorithm