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

K-edge-connected D-critical graphs of minimum order

Redistribution of vertices for maximum edge count in K-edge-connected D-critical graphs

Regularities in strings model many phenomena and thus form the subject of extensive mathematical studies [23]. Perhaps the most conspicuous regularities in strings are those that manifest themselves in the form of repeated subpatterns. In this paper, we study several forms of regularities of strings, that is, repeats, multirepeats, repetitions and runs. We present their similarities and differences by discussing their forms and properties and we explore the existing computation algorithms. We also discuss several data structures useful for computing regularities.

/pdf/computing-regularities-in-strings-30a8kuhjsp.pdf

Computing regularities in strings

In a string x on an alphabet @S, a position i is said to be indeterminate iff x[i] may be any one of a specified subset {@l"1,@l"2,...,@l"j} of @S, 2=

Fast pattern-matching on indeterminate strings

A parameterized string (p-string) is a generalization of the traditional string over two alphabets: a constant alphabet and a parameter alphabet. A parameterized match (p-match) exists between two p-strings if the constants match exactly and if there exists a bijection between the parameter symbols. Historically, p-strings have been leveraged for source code cloning, plagiarism detection, and biological sequence structural similarity. In this work, we identify the connection between the p-match and music, one of several applications to motivate our study of holes in p-strings, and prefix array-based data structures for p-strings. First, we introduce the parameterized prefix array (pPA) for p-strings and its succinct representation, the compact parameterized prefix array (cpPA). We show an interesting construction of the cpPA via the parameterized longest previous factor (pLPF), a more recently proposed array with connections to various pattern matching data structures and LZ factorization. Next, we introduce the parameterized string with holes (hp-string), needed to address a special form of indeterminate pattern matching with p-strings. Then, we show how to construct the compact prefix array for hp-strings. Finally, we discuss applications for our data structures.

William F. Smyth

Papers

K-edge-connected D-critical graphs of minimum order

Redistribution of vertices for maximum edge count in K-edge-connected D-critical graphs

Computing regularities in strings

Fast pattern-matching on indeterminate strings

A prefix array for parameterized strings