Exploiting non-constant safe memory in resilient algorithms and data structures

We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a safe memory of arbitrary size $S$, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let $\delta$ and $\alpha$ denote, respectively, the maximum amount of faults which can happen during the execution of an algorithm and the actual number of occurred faults, with $\alpha \leq \delta$. We propose a resilient algorithm for sorting $n$ entries which requires $O\left(n\log n+\alpha (\delta/S + \log S)\right)$ time and uses $\Theta(S)$ safe memory words. Our algorithm outperforms previous resilient sorting algorithms which do not exploit the available safe memory and require $O\left(n\log n+ \alpha\delta\right)$ time. Finally, we exploit our sorting algorithm for deriving a resilient priority queue. Our implementation uses $\Theta(S)$ safe memory words and $\Theta(n)$ faulty memory words for storing $n$ keys, and requires $O\left(\log n + \delta/S\right)$ amortized time for each insert and deletemin operation. Our resilient priority queue improves the $O\left(\log n + \delta\right)$ amortized time required by the state of the art.Comment: To appear in Theoretical Computer Science, 201

Co-occurrence Vectors from Corpora vs. Distance Vectors from Dictionaries

A comparison was made of vectors derived by using ordinary co-occurrence statistics from large text corpora and of vectors derived by measuring the inter-word distances in dictionary definitions. The precision of word sense disambiguation by using co-occurrence vectors from the 1987 Wall Street Journal (20M total words) was higher than that by using distance vectors from the Collins English Dictionary (60K head words + 1.6M definition words). However, other experimental results suggest that distance vectors contain some different semantic information from co-occurrence vectors.Comment: 6 pages, appeared in the Proc. of COLING94 (pp. 304-309)

Error-Correcting Data Structures

We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been corrupted by a constant fraction of errors. This new model is the common generalization of (static) data structures and locally decodable error-correcting codes. The main issue is the tradeoff between the space used by the data structure and the time (number of probes) needed to answer a query about the encoded object. We prove a number of upper and lower bounds on various natural error-correcting data structure problems. In particular, we show that the optimal length of error-correcting data structures for the Membership problem (where we want to store subsets of size s from a universe of size n) is closely related to the optimal length of locally decodable codes for s-bit strings.Comment: 15 pages LaTeX; an abridged version will appear in the Proceedings of the STACS 2009 conferenc

Scaling language competition in a small island state : graphic verbs in Seychellois Creole and English

One of the sensitive aspects of a small country is the predicament of its language. Seychellois Creole, one of that country`s three official languages and the native language of its Creole population, is asserting its linguistic identity against the globally-established English and French, the other two official languages of the country. How resilient is Seychellois Creole in this language triangle? Are the challenges it faces related to the small number of speakers, citizens of the small country? To what extent, and in what particular way, does Seychellois Creole vulnerable position, as a small language neighboured by two international languages, affect its development? These questions are approached in this paper by means of the comparative analysis of some linguistic parameters of Seychellois Creole and English. Research has been carried out with a group of English and Seychellois Creole verbs conceptualizing the process of graphic representation. The paper focuses on the capacity of the two contrasted languages for concept lexicalisation, patterns of semantic development and syntactic shifting.peer-reviewe