There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

/pdf/a-dynamic-survey-of-graph-labeling-198znmwxtq.pdf

A Dynamic Survey of Graph Labeling

The main way of analyzing biological sequences is by comparing and aligning them to each other. It remains difficult, however, to compare modern multi-billionbase DNA data sets. The difficulty is caused by the nonuniform (oligo)nucleotide composition of these sequences, rather than their size per se. To solve this problem, we modified the standard seed-and-extend approach (e.g., BLAST) to use adaptive seeds. Adaptive seeds are matches that are chosen based on their rareness, instead of using fixed-length matches. This method guarantees that the number of matches, and thus the running time, increases linearly, instead of quadratically, with sequence length. LAST, our open source implementation of adaptive seeds, enables fast and sensitive comparison of large sequences with arbitrarily nonuniform composition.

/pdf/adaptive-seeds-tame-genomic-sequence-comparison-58wsqwzwm9.pdf

Adaptive seeds tame genomic sequence comparison.

コンピュータ・サイエンス : ACM computing surveys

https://www.cs.usask.ca/~croy/papers/2009/RCK_SCP_Clones.pdf

Comparison and evaluation of code clone detection techniques and tools: A qualitative approach

In 1990, Manber and Myers proposed suffix arrays as a space-saving alternative to suffix trees and described the first algorithms for suffix array construction and use. Since that time, and especially in the last few years, suffix array construction algorithms have proliferated in bewildering abundance. This survey paper attempts to provide simple high-level descriptions of these numerous algorithms that highlight both their distinctive features and their commonalities, while avoiding as much as possible the complexities of implementation details. New hybrid algorithms are also described. We provide comparisons of the algorithms' worst-case time complexity and use of additional space, together with results of recent experimental test runs on many of their implementations.

/pdf/a-taxonomy-of-suffix-array-construction-algorithms-48rvbzufdz.pdf

A taxonomy of suffix array construction algorithms

A string is just a sequence of letters. But strings can be massive. Plant and animal genomes are strings billions of letters long on the simple alphabet Internet traffic among billions of websites is a collection of strings that amount to quadrillions of computer bits every day.

Such strings are regularly searched, probably millions of times a day, for patterns of all kinds - genomic codes for genes and chromosomes, indicators of terrorist activity, and many others. The search for patterns is fundamental to many fields molecular biology, cryptography, data compression, computer vision, speech recognition, computational geometry.

This book provides a basic general introduction to the algorithms (methods) that efficiently compute patterns in strings. It focuses on results that can be explained with reasonable economy and simplicity, but its 250 references also enable the reader to access current state-of-the-art methodology.

Computing Patterns in Strings

A fast and effective heuristic for the feedback arc set problem

Let x denote a given nonempty string of length n = |x| . A proper substring u of x is a proper cover of x if and only if every position of x lies within an occurrence of u within x . This paper introduces an array γ = γ[1..n] called the cover array in which each element γ[i] , 1 ≤ i ≤ n , is the length of the longest proper cover of x[1..i] or zero if no such cover exists. In fact it turns out that γ describes all the covers of every prefix of x . Several interesting properties of γ are established, and a simple algorithm is presented that computes γ on-line in Θ(n) time using Θ(n) additional space. Thus the new algorithm computes for all prefixes of x information that previous cover algorithms could compute only for x itself, and does so with no increase in space or time complexity.

/pdf/computing-the-cover-array-in-linear-time-2zmus7oy31.pdf

William F. Smyth

Papers

A taxonomy of suffix array construction algorithms

Computing Patterns in Strings

A fast and effective heuristic for the feedback arc set problem

Computing the Cover Array in Linear Time

A characterization of the squares in a Fibonacci string