We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs) We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task

The university of Florida sparse matrix collection

The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

Full-text indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text length. This concept has evolved into self-indexes, which in addition contain enough information to reproduce any text portion, so they replace the text. The exciting possibility of an index that takes space close to that of the compressed text, replaces it, and in addition provides fast search over it, has triggered a wealth of activity and produced surprising results in a very short time, which radically changed the status of this area in less than 5 years. The most successful indexes nowadays are able to obtain almost optimal space and search time simultaneously.In this article we present the main concepts underlying (compressed) self-indexes. We explain the relationship between text entropy and regularities that show up in index structures and permit compressing them. Then we cover the most relevant self-indexes, focusing on how they exploit text compressibility to achieve compact structures that can efficiently solve various search problems. Our aim is to give the background to understand and follow the developments in this area.

/pdf/compressed-full-text-indexes-4cxd0n1jff.pdf

Compressed full-text indexes

We introduce a new model of similarity of time sequences that captures the intuitive notion that two sequences should be considered similar if they have enough non-overlapping time-ordered pairs of subsequences thar are similar. The model allows the amplitude of one of the two sequences to be scaled by any suitable amount and its offset adjusted appropriately. Two subsequences are considered similar if one can be enclosed within an envelope of a specified width drawn around the other. The model also allows non-matching gaps in the matching subsequences. The matching subsequences need not be aligned along the time axis. Given this model of similarity, we present fast search techniques for discovering all similar sequences in a set of sequences. These techniques can also be used to find all (sub)sequences similar to a given sequence. We applied this matching system to the U.S. mutual funds data and discovered interesting matches.

/pdf/fast-similarity-search-in-the-presence-of-noise-scaling-and-a8g8tp0bi6.pdf

Fast Similarity Search in the Presence of Noise, Scaling, and Translation in Time-Series Databases

The proliferation of online text, such as found on the World Wide Web and in online databases, motivates the need for space-efficient text indexing methods that support fast string searching. We model this scenario as follows: Consider a text $T$ consisting of $n$ symbols drawn from a fixed alphabet $\Sigma$. The text $T$ can be represented in $n \lg |\Sigma|$ bits by encoding each symbol with $\lg |\Sigma|$ bits. The goal is to support fast online queries for searching any string pattern $P$ of $m$ symbols, with $T$ being fully scanned only once, namely, when the index is created at preprocessing time. The text indexing schemes published in the literature are greedy in terms of space usage: they require $\Omega(n \lg n)$ additional bits of space in the worst case. For example, in the standard unit cost RAM, suffix trees and suffix arrays need $\Omega(n)$ memory words, each of $\Omega(\lg n)$ bits. These indexes are larger than the text itself by a multiplicative factor of $\Omega(\smash{\lg_{|\Sigma|} n})$, which is significant when $\Sigma$ is of constant size, such as in \textsc{ascii} or \textsc{unicode}. On the other hand, these indexes support fast searching, either in $O(m \lg |\Sigma|)$ time or in $O(m + \lg n)$ time, plus an output-sensitive cost $O(\mathit{occ})$ for listing the $\mathit{occ}$ pattern occurrences. We present a new text index that is based upon compressed representations of suffix arrays and suffix trees. It achieves a fast $\smash{O(m /\lg_{|\Sigma|} n + \lg_{|\Sigma|}^\epsilon n)}$ search time in the worst case, for any constant $0 < \epsilon \leq 1$, using at most $\smash{\bigl(\epsilon^{-1} + O(1)\bigr) \, n \lg |\Sigma|}$ bits of storage. Our result thus presents for the first time an efficient index whose size is provably linear in the size of the text in the worst case, and for many scenarios, the space is actually sublinear in practice. As a concrete example, the compressed suffix array for a typical 100 MB \textsc{ascii} file can require 30--40 MB or less, while the raw suffix array requires 500 MB. Our theoretical bounds improve \emph{both} time and space of previous indexing schemes. Listing the pattern occurrences introduces a sublogarithmic slowdown factor in the output-sensitive cost, giving $O(\mathit{occ} \, \smash{\lg_{|\Sigma|}^\epsilon n})$ time as a result. When the patterns are sufficiently long, we can use auxiliary data structures in $O(n \lg |\Sigma|)$ bits to obtain a total search bound of $O(m /\lg_{|\Sigma|} n + \mathit{occ})$ time, which is optimal.

/pdf/compressed-suffix-arrays-and-suffix-trees-with-applications-1v4t8rnpc6.pdf

Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching

https://www.cs.colostate.edu/%7Ermm/linto.pdf

Modular decomposition and transitive orientation

Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

Given a finite set of texts S = {w1, … , wk} over some fixed finite alphabet S, a complete inverted file for S is an abstract data type that provides the functions find(w), which returns the longest prefix of w that occurs (as a subword of a word) in S; freq(w), which returns the number of times w occurs in S; and locations(w), which returns the set of positions where w occurs in S. A data structure that implements a complete inverted file for S that occupies linear space and can be built in linear time, using the uniform-cost RAM model, is given. Using this data structure, the time for each of the above query functions is optimal. To accomplish this, techniques from the theory of finite automata and the work on suffix trees are used to build a deterministic finite automaton that recognizes the set of all subwords of the set S. This automaton is then annotated with additional information and compacted to facilitate the desired query functions. The result is a data structure that is smaller and more flexible than the suffix tree.

/pdf/complete-inverted-files-for-efficient-text-retrieval-and-t3mzcr5l4e.pdf

Complete inverted files for efficient text retrieval and analysis

A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x , or no member of X is adjacent to x. There is a canonical linear-space representation for the modules of a graph, called the modular decomposition. The modular decomposition facilitates solution of a number of combinatorial problems on certain classes of graphs, and algorithms for computing it have a lengthy history. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive, if such an assignment is possible. We give the lirst linear-time algorithm for modular decomposition, and a new bound of 0 (ri +m logn) on transitive orientation and the problem of recognizing permutation graphs and two-dimensional partial orders.

/pdf/linear-time-modular-decomposition-and-efficient-transitive-3934c788xu.pdf

Linear-time modular decomposition and efficient transitive orientation of comparability graphs

An operational system for extracting ice-motion information from synthetic aperture radar (SAR) imagery is being developed as part of the Alaska SAR Facility. This geophysical processing system (GPS) will derive ice-motion information by automated analysis of image sequences acquired by radars on the European ERS-1, Japanese ERS-1, and Canadian RADARSAT remote sensing satellites. The algorithm consists of a novel combination of feature-based and area-based techniques for the tracking of ice floes that undergo translation and rotation between imaging passes. The system performs automatic selection of the image pairs for input to the matching routines using an ice-motion estimator. It is designed to have a daily throughput of ten image pairs. A description is given of the GPS system, including an overview of the ice-motion-tracking algorithm, the system architecture, and the ice-motion products that will be available for distribution to geophysical data users. >

Ross M. McConnell

Papers

Modular decomposition and transitive orientation

Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

Complete inverted files for efficient text retrieval and analysis

Linear-time modular decomposition and efficient transitive orientation of comparability graphs

An ice-motion tracking system at the Alaska SAR facility