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 this paper we extend previous work on unique maximal factorization families (UMFFs) and a total (but non-lexicographic) ordering of strings called VV-order. We present new combinatorial results for VV-order, in particular concatenation under VV-order. We propose linear-time RAM algorithms for string comparison in VV-order and for Lyndon-like factorization of a string into VV-words. This asymptotic efficiency thus matches that of the corresponding algorithms for lexicographical order. Finally, we introduce Hybrid Lyndon words as a generalization of standard Lyndon words, and hence propose extensions of factorization algorithms to other forms of order.

A linear partitioning algorithm for Hybrid Lyndons using -order

We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the third achieves linear time, but at the expense of prior computation of both the suffix array and the inverse suffix array of x. We then go on to describe two variants of a new algorithm that avoids prior computation of global data structures and executes in worst-case n log n time. Experimental evidence suggests that all but one of these five algorithms require only linear execution time in practice, with the two new algorithms faster by a small factor. We conjecture that there exists a fast and worst-case linear-time algorithm to compute the Lyndon array that is also elementary (making no use of global data structures such as the suffix array).

Algorithms to Compute the Lyndon Array

Hybrid pattern-matching algorithms on indeterminate strings

For certain problems (for example, computing repetitions and repeats, data compression applications) it is not necessary that the suffixes of a string represented in a suffix tree or suffix array should occur in lexicographical order (lexorder). It thus becomes of interest to study possible alternate orderings of the suffixes in these data structures, that may be easier to construct or more efficient to use. In this paper we consider the "reconstruction" of a suffix array based on a given reordering of the alphabet, and we describe simple time- and space-efficient algorithms that accomplish it.

/pdf/reconstructing-a-suffix-array-3vxfwalx8a.pdf

Reconstructing a suffix array

spambots are a new type of internet robot that spread spam content through Web 2.0 applications like online discussion boards, blogs, wikis, social networking platforms etc. These robots are intelligently designed to act like humans in order to fool safeguards and other users. Such spam content not only wastes valuable resources and time but also may mislead users with unsolicited content. Spam content typically intends to misinform users (scams), generate traffic, make sales (marketing/advertising), and occasionally compromise parties, people or systems by spreading spyware or malwares. Current countermeasures do not effectively identify and prevent web spambots. Proactive measures to deter spambots from entering a site are limited to question / response scenarios. The remaining efforts then focus on spam content identification as a passive activity. Spammers have evolved their techniques to bypass existing anti-spam filters. In this paper, we describe a rule-based web usage behaviour action string that can be analysed using Trie data structures to detect web spambots. Our experimental results show the proposed system is successful for on-the-fly classification of web spambots hence eliminating spam in web 2.0 applications.

/pdf/rule-based-on-the-fly-web-spambot-detection-using-action-b2gpxkuimz.pdf

William F. Smyth

Papers

A linear partitioning algorithm for Hybrid Lyndons using -order

Algorithms to Compute the Lyndon Array

Hybrid pattern-matching algorithms on indeterminate strings

Reconstructing a suffix array

Rule-Based On-the-fly Web Spambot Detection Using Action Strings