We survey the current techniques to cope with the problem of string matching that allows errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices. We conclude with some directions for future work and open problems.

/pdf/a-guided-tour-to-approximate-string-matching-22fowlmq5b.pdf

A guided tour to approximate string matching

An algorithm for drawing general undirected graphs

An edited volume containing data structures and algorithms for information retrieved including a disk with examples written in C. For programmers and students interested in parsing text, automated indexing, its the first collection in book form of the basic data structures and algorithms that are critical to the storage and retrieval of documents.

https://hornad.fei.tuke.sk/~genci/Vyucba/OOBDS/Archiv/Podklady/TExtoveIS&IR/Information%20Retrieval%20Data%20Structures%20&%20Algorithms.PDF

Information Retrieval: Data Structures and Algorithms

FFT literature has been mostly concerned with minimizing the number of floating-point operations performed by an algorithm. Unfortunately, on present-day microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have a larger impact on performance. Consequently, one must know the details of a computer architecture in order to design a fast algorithm. In this paper, we propose an adaptive FFT program that tunes the computation automatically for any particular hardware. We compared our program, called FFTW, with over 40 implementations of the FFT on 7 machines. Our tests show that FFTW's self-optimizing approach usually yields significantly better performance than all other publicly available software. FFTW also compares favorably with machine-specific, vendor-optimized libraries.

/pdf/fftw-an-adaptive-software-architecture-for-the-fft-1isptvhgfa.pdf

FFTW: an adaptive software architecture for the FFT

The FFTW library for computing the discrete Fourier transform (DFT) has gained a wide acceptance in both academia and industry, because it provides excellent performance on a variety of machines (even competitive with or faster than equivalent libraries supplied by vendors). In FFTW, most of the performance-critical code was generated automatically by a special-purpose compiler, called genfft, that outputs C code. Written in Objective Caml, genfft can produce DFT programs for any input length, and it can specialize the DFT program for the common case where the input data are real instead of complex. Unexpectedly, genfft "discovered" algorithms that were previously unknown, and it was able to reduce the arithmetic complexity of some other existing algorithms. This paper describes the internals of this special-purpose compiler in some detail, and it argues that a specialized compiler is a valuable tool.

/pdf/a-fast-fourier-transform-compiler-4w0zmnryds.pdf

A fast Fourier transform compiler

A new upper bound on the complexity of the all pairs shortest path problem

http://theory.stanford.edu/~virgi/cs367/papers/maxsubarray.pdf

Efficient Algorithms for the Maximum Subarray Problem by Distance Matrix Multiplication

An algorithm is described that solves the all pairs shortest path problem for a nonnegatively weighted directed graph of n vertices in average time $O(n^2 \log n)$. The algorithm is a blend of two previous shortest path algorithms, those of Dantzig [Management Sci., 6 (1960), pp. 187–190] and Spira [SIAM J. Comput., 2 (1973), pp. 28–32]. Bloniarz [SIAM J. Comput., 12 (1983), pp. 588–600] categorised a class of random graphs called endpoint independent graphs; the new algorithm executes in the stated time on endpoint independent graphs and represents an asymptotic improvement over the $O(n^2 \log n\log ^ * n)$ algorithm given by Bloniarz for this class of random graphs.

An all pairs shortest path algorithm with expected time O ( n 2 log n )

In this paper we give three subcubic cost algorithms for the all pairs shortest distance (APSD) and path (APSP) problems. The first is a parallel algorithm that solves the APSD problem for a directed graph with unit edge costs in O(log

 2
 
n) time with $O(n^\mu/\sqrt{\log n})$ processors where μ = 2.688 on an EREW PRAM. The second parallel algorithm solves the APSP, and consequently APSD, problem for a directed graph with nonnegative general costs (real numbers) in O(log

 2
 
n) time with o(n

 3
 
) subcubic cost. Previously this cost was greater than O(n

 3
 
) . Finally we improve with respect to M the complexity O((Mn)

 μ
 
) of a sequential algorithm for a graph with edge costs up to M to O(M

 1/3
 
n

 (6+ω)/3
 
(log n)

 2/3
 
(log log n)

 1/3
 
) in the APSD problem, where ω = 2.376 .

/pdf/subcubic-cost-algorithms-for-the-all-pairs-shortest-path-1uq9pm5cgu.pdf

Subcubic Cost Algorithms for the All Pairs Shortest Path Problem

By reducing an array matching problem to a string matching problem in a natural way, it is shown that efficient string matching algorithms can be applied to arrays, assuming that a linear preprocessing is made on the text.

Tadao Takaoka

Papers

A new upper bound on the complexity of the all pairs shortest path problem

Efficient Algorithms for the Maximum Subarray Problem by Distance Matrix Multiplication

An all pairs shortest path algorithm with expected time O ( n 2 log n )

Subcubic Cost Algorithms for the All Pairs Shortest Path Problem

A technique for two-dimensional pattern matching