RAM-Efficient External Memory Sorting

In recent years a large number of problems have been considered in external memory models of computation, where the complexity measure is the number of blocks of data that are moved between slow external memory and fast internal memory (also called I/Os). In practice, however, internal memory time often dominates the total running time once I/O-efficiency has been obtained. In this paper we study algorithms for fundamental problems that are simultaneously I/O-efficient and internal memory efficient in the RAM model of computation.Comment: To appear in Proceedings of ISAAC 2013, getting the Best Paper Awar

Space efficient algorithms for string processing

The suffix array (SA), which is an array containing the suffixes of a string sorted into lexicographical order, was introduced in the late eighties as a space efficient alternative to the suffix tree. It has since emerged as a useful data structure in string processing problems such as pattern matching, pattern discovery, and data compression. The SA is often coupled with the longest-common-prefix (LCP) array that contains the length of the longest common prefixes between consecutive suffixes in the SA. When enhanced with the LCP array, the SA can provide efficient solutions to the above applications including a problem called pattern mining. To date, all the mining algorithms lie at either extreme of the efficiency spectrum: they are either fast and use enormous amounts of space, or they are compact and orders of magnitude slower. We present a mining algorithm that achieves the best of both these extremes, having runtime comparable to the fastest published algorithms while using less space than the most space efficient. In all these applications, the construction of the SA --- also known as suffix sorting --- is one of the main computational bottlenecks. Most papers describing the SA assume the SA fits in RAM memory, limiting their applications. The fastest algorithms in this large memory suffix sorting category use powerful pointer copying heuristics to expedite suffix sorting. Several space efficient algorithms have emerged in the last five years, where the trend is to use as little RAM as possible. They do so by finding a clever way to trade runtime, or by using slow compressed data structures, or by using external memory (disk), or some combination of these techniques. In this thesis, we focus on improving the runtime of a space efficient algorithm due to Kärkkäinen by adapting the heuristics from large memory suffix sorting to a semi-external setting. Also, pointer copying has been heavily used to speed up the construction of the SA, but not the LCP array. We also discuss our attempts of combining the pointer copying heuristics to an efficient LCP construction algorithm due to Kärkkäinen, Manzini and Puglisi. The Burrows-Wheeler transform (BWT) was discovered independently of the SA, but it is now known that the two data structures are deeply linked. The BWT is central to practical compression tools such as szip and bzip2. Many papers have been published on constructing the BWT either in RAM or in external memory but few on inverting the BWT to obtain the original string --- in fact none in external memory. For larger datasets, the existing traditional approaches cannot be used to invert the BWT. In such cases, we have to use disk. We close the gap between theory and practice by examining the problem of inverting the BWT efficiently on disk. We provide a practical implementation of the only theoretical proposal for the problem by Ferragina, Gagie and Manzini. We also provide new, faster solutions to the problem based on simple scanning and compression techniques

A Bulk-Parallel Priority Queue in External Memory with STXXL

We propose the design and an implementation of a bulk-parallel external memory priority queue to take advantage of both shared-memory parallelism and high external memory transfer speeds to parallel disks. To achieve higher performance by decoupling item insertions and extractions, we offer two parallelization interfaces: one using "bulk" sequences, the other by defining "limit" items. In the design, we discuss how to parallelize insertions using multiple heaps, and how to calculate a dynamic prediction sequence to prefetch blocks and apply parallel multiway merge for extraction. Our experimental results show that in the selected benchmarks the priority queue reaches 75% of the full parallel I/O bandwidth of rotational disks and and 65% of SSDs, or the speed of sorting in external memory when bounded by computation.Comment: extended version of SEA'15 conference pape

Empirical Evaluation of the Parallel Distribution Sweeping Framework on Multicore Architectures

In this paper, we perform an empirical evaluation of the Parallel External Memory (PEM) model in the context of geometric problems. In particular, we implement the parallel distribution sweeping framework of Ajwani, Sitchinava and Zeh to solve batched 1-dimensional stabbing max problem. While modern processors consist of sophisticated memory systems (multiple levels of caches, set associativity, TLB, prefetching), we empirically show that algorithms designed in simple models, that focus on minimizing the I/O transfers between shared memory and single level cache, can lead to efficient software on current multicore architectures. Our implementation exhibits significantly fewer accesses to slow DRAM and, therefore, outperforms traditional approaches based on plane sweep and two-way divide and conquer.Comment: Longer version of ESA'13 pape

Data-Oblivious Graph Algorithms in Outsourced External Memory

Motivated by privacy preservation for outsourced data, data-oblivious external memory is a computational framework where a client performs computations on data stored at a semi-trusted server in a way that does not reveal her data to the server. This approach facilitates collaboration and reliability over traditional frameworks, and it provides privacy protection, even though the server has full access to the data and he can monitor how it is accessed by the client. The challenge is that even if data is encrypted, the server can learn information based on the client data access pattern; hence, access patterns must also be obfuscated. We investigate privacy-preserving algorithms for outsourced external memory that are based on the use of data-oblivious algorithms, that is, algorithms where each possible sequence of data accesses is independent of the data values. We give new efficient data-oblivious algorithms in the outsourced external memory model for a number of fundamental graph problems. Our results include new data-oblivious external-memory methods for constructing minimum spanning trees, performing various traversals on rooted trees, answering least common ancestor queries on trees, computing biconnected components, and forming open ear decompositions. None of our algorithms make use of constant-time random oracles.Comment: 20 page