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

A number of approaches to the measurement of program quality or ‘style’ have recently been described in the computing literature. This article discusses criteria which may be considered for the evaluation of these and other approaches, and for the development of new ones.

Evaluating measures of program quality

Given a string x = x[1..n], a repetition of period p in x is a substring ur = x[i..i+rp−1], p = |u|, r ≥ 2, where neither u = x[i..i+p−1] nor x[i..i+(r+1)p−1] is a repetition. The maximum number of repetitions in any string x is well known to be Θ(n log n). A run or maximal periodicity of period p in x is a substring urt = x[i..i+rp+|t|−1] of x, where ur is a repetition, t a proper prefix of u, and no repetition of period p begins at position i−1 of x or ends at position i+rp+|t|. In 2000 Kolpakov & Kucherov showed that the maximum number ρ(n) of runs in any string x is O(n), but their proof was nonconstructive and provided no specific constant of proportionality. At the same time, they presented experimental data strongly suggesting that ρ(n) < n. that the maximum any string x again encourages the belief that in fact σ(n) < n. Recently, Fan et al.(“A new periodicity lemma”, Sixteenth Annual Symp. Combin. Pattern Matching, 2005) took a first step toward proving these conjectures, by presenting results that establish limitations on the number of squares of a specified range of periods that can occur over a specified range of positions in x. In this paper, we further tighten these restrictions by showing how the existence of two squares u and v (v longer than u) at the same position i in x limits the occurrence of smaller squares with period w ∈ (|v| − |u|, |u|) in the neighborhood around i.

Some restrictions on periodicity in strings

This paper describes a strategy for content-based image retrieval via spatial configuration of objects within an image. The proposed strategy locates “pattern” images within “text” images, where the objects in each image are specified only in terms of their pairwise spatial relationships. Thus both pattern and text are represented by square matrices whose elements are drawn from an “alphabet” of spatial relationships. A match is found when the pattern image is identified as a “substructure” of a given text image. Experimental results relating to retrieval of images with low image content are shown. The approach can be used in situations where methods involving features such as colours and texture are inappropriate. We believe that such algorithms would find application in topological/GIS applications where the aerial/satellite images are very similar in terms of low-level image content.

/pdf/heuristics-for-image-retrieval-using-spatial-configurations-15cz73x352.pdf

Heuristics for image retrieval using spatial configurations

We study a central problem of string processing: the compact representation of a string by its frequently-occurring substrings. In this paper we propose an effective, easily-computed form of quasi-periodicity in strings, the frequency cover; that is, the longest of those repeating substrings u of w, |u| > 1, that occurs the maximum number of times in w. The advantage of this generalization is that it is not only applicable to all strings but also that it is the only generalized notion of cover yet proposed, which can be computed efficiently in linear time and space. We describe a simple data structure called the repeating substring frequency array (ℛ

Frequency Covers for Strings

A factor u of a string y is a cover of y if every letter of y lies within some occurrence of u in y; thus every cover u is also a border – both prefix and suffix – of y. A string y covered by u thus generalises the idea of a repetition; that is, a string composed of exact concatenations of u. Even though a string is coverable somewhat more frequently than it is a repetition, still a string that can be covered by a single u is rare. As a result, seeking to find a more generally applicable and descriptive notion of cover, many articles were written on the computation of a minimum k-cover of y; that is, the minimum cardinality set of strings of length k that collectively cover y. Unfortunately, this computation turns out to be NP-hard. Therefore, in this article, we propose new, simple, easily-computed, and widely applicable notions of string covering that provide an intuitive and useful characterisation of a string and its prefixes: the enhanced cover and the enhanced cover array.

/pdf/new-and-efficient-approaches-to-the-quasiperiodic-1hawqafz6g.pdf

William F. Smyth

Papers

Evaluating measures of program quality

Some restrictions on periodicity in strings

Heuristics for image retrieval using spatial configurations

Frequency Covers for Strings

New and efficient approaches to the quasiperiodic characterisation of a string