Approximate searching using an index is an important application in many fields. In this paper we introduce a new data structure called the gapped suffix array for approximate searching in the Hamming distance model. Building on the well known filtration approach for approximate searching, the use of the gapped suffix array can improve search speed by avoiding the merging of position lists.

For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...

We study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal suffix of a string, which is a basic ingredient in many other problems. We first revisit two special cases of the problem, introduced by Babenko, Kolesnichenko...

This paper consider the problem of search engine that are not capable of retrieving appropriate result on query given. Most of the users are not able to give the appropriate query to get what exactly they wanted to retrieve. So the search engine retrieves a massive list of data, which are ranked by the page rank algorithm or relevancy algorithm or human judgment algorithm. If the relevant resul...

Suffix trees are the most frequently used data structures in algorithms on words. In this paper, we consider the depth of a compact suffix tree, also known as the PAT tree, under some simple probabilistic assumptions. For a biased memoryless source, we prove that the limiting distribution for the depth in a PAT tree is the same as the limiting distribution for the depth in a PATRICIA trie, even...

Let τ be a fixed lattice path (called in this context string) on the integer plane, consisting of two kinds of steps. The Dyck path statistic “number of occurrences of τ” has been studied by many authors, for particular strings only. In this paper, arbitrary strings are considered. The associated generating function is evaluated when τ is a Dyck prefix (or a Dyck suffix). Furthermore, the case ...

in the recent theory of generative grammar there are two major views on case assignment. the standard chomskyan view stats that case is assigned by the grammatical head to the closest np through an agreement relationship (baker, 2010). in this approach case has a purely syntactic notion as a case assigner and is directly related to structural cases and structural relations of case receiving nps...

Documents in HTML format have many features to analyze, from the terms in special sections to the phrases that appear in the whole document. However, it is important to decide which feature contributes the most to separate documents according to classes. Given this information, it is possible not to include certain feature in the representation for the document, given that it is expensive to co...

Surprisingly enough, it is not yet known how to build directly a suffix array that indexes just the k positions at word-boundaries of a text T [1, n], taking O(n) time and O(k) space in addition to T . We propose a class-note solution to this problem that achieves such optimal time and space bounds. Word-based versions of indexes achieving the same time/space bounds were already known for suffi...

The suffix tree is a very powerful data structure developed originally for string matching and string searching. It has found many applications over the time and some of them belong into the data compression field. Many of these applications need a suffix tree built for a sliding window and there exist two clever algorithms by Fiala and Greene and by Larsson that make this possible. However, as...