Rahul Shah

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We present $$O(n)$$ O ( n ) -space data structures to support various range frequency queries on a given array $$A[0:n-1]$$ A [ 0 : n - 1 ] or tree $$T$$ T with $$n$$ n nodes. Given a query consisting of an arbitrary pair of pre-order rank indices $$(i,j)$$ ( i , j ) , our data structures return a least frequent element, mode, $$\alpha $$ α -minority, or(More)
We introduce a new variant of the popular Burrows-Wheeler transform (BWT), called Geometric Burrows-Wheeler Transform (GBWT), which converts a text into a set of points in 2-dimensional geometry. We also introduce a reverse transform, called Points2Text, which converts a set of points into text. Using these two transforms, we show strong equivalence between(More)
We consider a central problem in text indexing: Given a text T over an alphabet Σ, construct a compressed data structure answering the queries char (i), rank s (i), and select s (i) for a symbol s ∈ Σ. Many data structures consider these queries for static text T [GGV03, FM01, SG06, GMR06]. We consider the dynamic version of the problem, where we are(More)
Let $$\mathcal {D} = \{\mathsf {T}_1,\mathsf {T}_2, \ldots ,\mathsf {T}_D\}$$ D = { T 1 , T 2 , … , T D } be a collection of D string documents of n characters in total, that are drawn from an alphabet set $$\varSigma =[\sigma ]$$ Σ = [ σ ] . The top-k document retrieval problem is to preprocess $$\mathcal{D}$$ D into a data structure that, given a query(More)
We provide a model and some solution techniques for some problems arising in the design of survivable telecommunication networks utilizing ber-optics based techniques. Given a set of network nodes and a set of possible links between them, we decide where to build links and where to place multiplexers. For this architecture to be survivable, we use ring(More)
Given a set $\mathcal{D}$ of patterns of total length n, the dictionary matching problem is to index $\mathcal{D}$ such that for any query text T, we can locate the occurrences of any pattern within T efficiently. This problem can be solved in optimal O(|T|+occ) time by the classical AC automaton (Aho and Corasick in Commun. ACM 18(6):333–340, 1975), where(More)
Content-Based Multicast is a type of multicast where the source sends a set of diierent classes of information and not all the subscribers in the multicast group need all the information. Use of ltering publish-subscribe agents on the intermediate nodes was suggested 5] to lter out the unnecessary information on the multicast tree. However, lters have their(More)
Many optimization problems which are known to be NP-hard on graphs are polynomially solvable on trees using dynamic programming. Dynamic programming typically involves recursive functions stored as tables. Each entry of the table corresponds to the optimal subproblem solution. In many applications the complexity of brute-force dynamic programming can be(More)