Optimal-Time Text Indexing in BWT-runs Bounded Space

Indexing highly repetitive texts --- such as genomic databases, software repositories and versioned text collections --- has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts is $r$, the number of runs in their Burrows-Wheeler Transform (BWT). One of the earliest indexes for repetitive collections, the Run-Length FM-index, used $O(r)$ space and was able to efficiently count the number of occurrences of a pattern of length $m$ in the text (in loglogarithmic time per pattern symbol, with current techniques). However, it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of $r$. Since then, a number of other indexes with space bounded by other measures of repetitiveness --- the number of phrases in the Lempel-Ziv parse, the size of the smallest grammar generating the text, the size of the smallest automaton recognizing the text factors --- have been proposed for efficiently locating, but not directly counting, the occurrences of a pattern. In this paper we close this long-standing problem, showing how to extend the Run-Length FM-index so that it can locate the $occ$ occurrences efficiently within $O(r)$ space (in loglogarithmic time each), and reaching optimal time $O(m+occ)$ within $O(r\log(n/r))$ space, on a RAM machine of $w=\Omega(\log n)$ bits. Within $O(r\log (n/r))$ space, our index can also count in optimal time $O(m)$. Raising the space to $O(r w\log_\sigma(n/r))$, we support count and locate in $O(m\log(\sigma)/w)$ and $O(m\log(\sigma)/w+occ)$ time, which is optimal in the packed setting and had not been obtained before in compressed space. We also describe a structure using $O(r\log(n/r))$ space that replaces the text and extracts any text substring of length $\ell$ in almost-optimal time $O(\log(n/r)+\ell\log(\sigma)/w)$. (...continues...

Batch Verification of Short Signatures

With computer networks spreading into a variety of new environments, the need to authenticate and secure communication grows. Many of these new environments have particular requirements on the applicable cryptographic primitives. For instance, several applications require that communication overhead be small and that many messages be processed at the same time. In this paper we consider the suitability of public key signatures in the latter scenario. That is, we consider signatures that are 1) short and 2) where many signatures from (possibly) different signers on (possibly) different messages can be verified quickly. Prior work focused almost exclusively on batching signatures from the same signer. We propose the first batch verifier for messages from many (certified) signers without random oracles and with a verification time where the dominant operation is independent of the number of signatures to verify. We further propose a new signature scheme with very short signatures, for which batch verification for many signers is also highly efficient. Combining our new signatures with the best known techniques for batching certificates from the same authority, we get a fast batch verifier for certificates and messages combined. Although our new signature scheme has some restrictions, it is very efficient and still practical for some communication applications

A Survey to Fix the Threshold and Implementation for Detecting Duplicate Web Documents

The drastic development in the information accessible on the World Wide Web has made the employment of automated tools to locate the information resources of interest, and for tracking and analyzing the same a certainty. Web Mining is the branch of data mining that deals with the analysis of World Wide Web. The concepts from various areas such as Data Mining, Internet technology and World Wide Web, and recently, Semantic Web can be said as the origin of web mining. Web mining can be defined as the procedure of determining hidden yet potentially beneficial knowledge from the data accessible in the web. Web mining comprise the sub areas: web content mining, web structure mining, and web usage mining. Web content mining is the process of mining knowledge from the web pages besides other web objects. The process of mining knowledge about the link structure linking web pages and some other web objects is defined as Web structure mining. Web usage mining is defined as the process of mining the usage patterns created by the users accessing the web pages. The search engine technology has led to the development of World Wide. The search engines are the chief gateways for access of information in the web. The ability to locate contents of particular interest amidst a huge heap has turned businesses beneficial and productive. The search engines respond to the queries by employing the process of web crawling that populates an indexed repository of web pages. The programs construct a confined repository of the segment of the web that they visit by navigating the web graph and retrieving pages. There are two main types of crawling, namely, Generic and Focused crawling. Generic crawlers crawls documents and links of diverse topics. Focused crawlers limit the number of pages with the aid of some prior obtained specialized knowledge. The systems that index, mine, and otherwise analyze pages (such as, the search engines) are provided with inputs from the repositories of web pages built by the web crawlers. The drastic development of the Internet and the growing necessity to incorporate heterogeneous data is accompanied by the issue of the existence of near duplicate data. Even if the near duplicate data don’t exhibit bit wise identical nature they are remarkably similar. The duplicate and near duplicate web pages either increase the index storage space or slow down or increase the serving costs which annoy the users, thus causing huge problems for the web search engines. Hence it is inevitable to design algorithms to detect such pages