We study the non-overlapping indexing problem: Given a text T, preprocess it so that you can answer queries of the form: given a pattern P, report the maximal set of non-overlapping occurrences of P in T. A generalization of this problem is the range non-overlapping indexing where in addition we are given two indexes i,j to report the maximal set of non-overlapping occurrences between these two indexes. We suggest new solutions for these problems. For the non-overlapping problem our solution uses O(n) space with query time of O(m + occ_{NO}). For the range non-overlapping problem we propose a solution with O(n\log^εn) space for some 0<ε<1 and O(m + \log\log n + occ_{ij,NO}) query time.
Text indexing, the problem in which one desires to preprocess a (usually large) text for future (shorter) queries, has been researched ever since the suffix tree was invented in the early 70's. With textual data continuing to increase and with changes in the way it is accessed, new data structures and new algorithmic methods are continuously required. Therefore, text indexing is of utmost importance and is a very active research domain. Orthogonal range searching, classically associated with the computational geometry community, is one of the tools that has increasingly become important for va…
Traditional indexing techniques commonly employed in da\-ta\-ba\-se systems perform poorly on multidimensional array scientific data. Bitmap indices are widely used in commercial databases for processing complex queries, due to their effective use of bit-wise operations and space-efficiency. However, bitmap indices apply natively to relational or linearized datasets, which is especially notable in binned or compressed indices. We propose a new method for multidimensional array indexing that overcomes the dimensionality-induced inefficiencies. The hierarchical indexing method is based on $n$-di…
Overlap is a common phenomenon seen when structural components of a digital object are neither disjoint nor nested inside each other. Overlapping components resist reduction to a structural hierarchy, and tree-based indexing and query processing techniques cannot be used for them. Our solution to this data modeling problem is TGSA (Tree-like Graph for Structural Annotations), a novel extension of the XML data model for non-hierarchical structures. We introduce an algorithm for constructing TGSA from annotated documents; the algorithm can efficiently process non-hierarchical structures and is a…
We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results. {itemize} We give efficient reductions for each of the above problems to a new problem, which we call \emph{substring range reporting}. Hence, we unify the previous work by showing that we may restrict our attention to a single problem rather than studying each of the above problems individually. We show how to solve substring range reporting with optimal query tim…
Under the word RAM model, we design three data structures that can be constructed in $O(n\sqrt{\lg n})$ time over $n$ points in an $n \times n$ grid. The first data structure is an $O(n\lg^ε n)$-word structure supporting orthogonal range reporting in $O(\lg\lg n+k)$ time, where $k$ denotes output size and $ε$ is an arbitrarily small constant. The second is an $O(n\lg\lg n)$-word structure supporting orthogonal range successor in $O(\lg\lg n)$ time, while the third is an $O(n\lg^ε n)$-word structure supporting sorted range reporting in $O(\lg\lg n+k)$ time. The query times of these data structu…
The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting queries (return all positions where the pattern occurs), and counting queries (return the number of occurrences of the pattern). In this paper we consider a variant of string indexing, where the goal is to compactly represent the string such that given two patterns P1 and P2 and a gap range [α,β] we can quickly find the consecutive occurrences of P1 and P2 with d…
Bille and Gørtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string $S$ of $n$ characters with integer labels in ([0, u]), such that later, given an interval ([a, b]) and a pattern $P$ of length $m$, we can quickly count the occurrences of $P$ whose first characters' labels are in ([a, b]). They showed how to store $S$ in $\Oh{n \log n / \log \log n}$ space and answer queries in $\Oh{m + \log \log u}$ time. We show that, if $S$ is over an alphabet of size (\polylog (n)), then we can achieve optimal linear space. Moreover, if (u…
Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time for polynomially sized alphabets. However, when it comes to answering queries with worst-case deterministic time bounds, the prior does so in $O(m\log|Σ|)$ time, where $m$ is the query size, $|Σ|$ is the alphabet size, and the latter does so in $O(m+\log n)$ time, where $n$ is the text size. If one wants to output all appearances of the query, an additive cost of $O(occ)$ time is sufficient, where $occ$ is the size of the output. We prop…
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l; a_r]}. Secondary indexes are heavily used in relational databases and scientific data analysis. It is well-known that the obvious solution, storing a dictionary for the position set associated with each character, does not always give optimal query time. In this paper we give the first theoretically optimal data structure for the secondary indexing problem. In t…
We have attempted in this paper to reduce the number of checked condition through saving frequency of the tandem replicated words, and also using non-overlapping iterative neighbor intervals on plane sweep algorithm. The essential idea of non-overlapping iterative neighbor search in a document lies in focusing the search not on the full space of solutions but on a smaller subspace considering non-overlapping intervals defined by the solutions. Subspace is defined by the range near the specified minimum keyword. We repeatedly pick a range up and flip the unsatisfied keywords, so the relevant ra…
Finding trajectories and discovering motifs that are similar in large datasets is a central problem for a wide range of applications. Solutions addressing this problem usually rely on spatial indexing and on the computation of a similarity measure in polynomial time. Although effective in the context of sparse trajectory datasets, this approach is too expensive in the context of dense datasets, where many trajectories potentially match with a given query. In this paper, we apply fingerprinting, a copy-detection mechanism used in the context of textual data, to trajectories. To this end, we fin…
Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose novel and efficient in-memory indexing techniques for intervals, with a focus on interval range queries, which are a basic component of many search and analysis tasks. First, we propose an optimized version of a single-level (flat) domain-partitioning approach, which may have large space requirements due to excessive replication. Then, we propose a hierarchic…
With the recent explosion of publicly available biological data, the analysis of networks has gained significant interest. In particular, recent promising results in Neuroscience show that the way neurons and areas of the brain are connected to each other plays a fundamental role in cognitive functions and behaviour. Revealing pattern and structures within such an intricate volume of connections is a hard problem that has its roots in Graph and Network Theory. Since many real world situations can be modelled through networks, structures detection algorithms find application in almost every fie…
