Copyright (c) 2010 All rights reserved. http://works.bepress.com/ankur_gupta Recent documents in Ankur Gupta en-us Thu, 06 May 2010 07:45:10 PDT 3600 http://works.bepress.com/ankur_gupta/10 http://works.bepress.com/ankur_gupta/10 Thu, 25 Feb 2010 10:48:42 PST Interaction between transport and reaction generates a variety of complex spatio-temporal patterns in chemical reactors. These patterned states, which are typically initiated by autocatalytic effects and sustained by differences in diffusion/local mixing rates, often cause undesired effects in the reactor. In this work, we analyze the dynamic evolution of mixing-limited spatial pattern formation in fast, homogeneous autocatalytic reactions occurring in isothermal tubular reactors using two-dimensional (2-D) convection-diffusion-reaction (CDR) models that are obtained through rigorous spatial averaging of the three-dimensional (3-D) CDR model using Liapunov-Schmidt technique of bifurcation theory. We use the spatially-averaged 2-D CDR model (and its "regularized" form) to perform steady-state bifurcation analysis that captures the region of multiple solutions, and we analyze the stability of these multiple steady states to transverse perturbations using linear stability analysis. Parametric analyses of the steady-state bifurcation diagrams and stability boundaries show that when transverse mixing is significantly slower than the rate of autocatalytic reaction, mixing-limited patterns emerge from the unstable middle branch that connects the ignition and extinction points of an S-shaped bifurcation curve. Our dynamic simulations show the emergence of three different types of spatial patterns namely, Band, Anti-phase and Target, depending on the nature of transverse perturbation. The temporal evolution of these patterns consists of rapid intensification of the concentration-segregation process (especially when transverse mixing is much slower than reaction) followed by slow diffusion-mediated return to symmetry that occurs at time scales much larger than the reactor residence time. Our parametric analysis of the dynamics reveals that while larger Péclet numbers (both axial and transverse) increase the stability and decay time of the patterned states, larger Damköhler numbers lead to faster ignition resulting in the opposite effect. Ankur Gupta Chemical Reaction Engineering http://works.bepress.com/ankur_gupta/9 http://works.bepress.com/ankur_gupta/9 Thu, 25 Feb 2010 10:26:05 PST We present a framework to dynamize succinct data structures, to encourage their use over non-succinct versions in a wide variety of important application areas. Our framework can dynamize most stateof-the-art succinct data structures for dictionaries, ordinal trees, labeled trees, and text collections. Ankur Gupta http://works.bepress.com/ankur_gupta/7 http://works.bepress.com/ankur_gupta/7 Wed, 24 Feb 2010 07:26:34 PST In this paper, we present an experimental study of the spacetime tradeoffs for the dictionary problem, where we design a data structure to represent set data, which consist of a subset S of n items out of a universe U = {0, 1,...,u − 1} supporting various queries on S. Our primary goal is to reduce the space required for such a dictionary data structure. Many compression schemes have been developed for dictionaries, which fall generally in the categories of combinatorial encodings and data-aware methods and still support queries efficiently. We show that for many (real-world) datasets, data-aware methods lead to a worthwhile compression over combinatorial methods. Additionally, we design a new data-aware building block structure called BSGAP that presents improvements over other data-aware methods. Ankur Gupta http://works.bepress.com/ankur_gupta/6 http://works.bepress.com/ankur_gupta/6 Wed, 24 Feb 2010 07:23:42 PST We report on a new and improved version of high-order entropy-compressed suffix arrays, which has theoretical performance guarantees similar to those in our earlier work [16], yet represents an improvement in practice. Our experiments indicate that the resulting text index offers state-of-the-art compression. In particular, we require roughly 20 % of the original text size--without requiring a separate instance of the text--and support fast and powerful searches. To our knowledge, this is the best known method in terms of space for fast searching. 1 Roberto Grossi http://works.bepress.com/ankur_gupta/5 http://works.bepress.com/ankur_gupta/5 Wed, 24 Feb 2010 07:09:48 PST We propose measures for compressed data structures, in which space usage is measured in a data-aware manner. In particular, we consider the fundamental dictionary problem on set data, where the task is to construct a data structure to represent a set S of n items out of a universe U = {0,..., u − 1} and support various queries on S. We use a well-known data-aware measure for set data called gap to bound the space of our data structures. We describe a novel dictionary structure taking gap+O(n log(u/n) / log n)+O(n log log(u/n)) bits. Under the RAM model, our dictionary supports membership, rank, select, and predecessor queries in nearly optimal time, matching the time bound of Andersson and Thorup's predecessor structure [AT00], while simultaneously improving upon their space usage. Our dictionary structure uses exactly gap bits in the leading term (i.e., the constant factor is 1) and answers queries in near-optimal time. When seen from the worst case perspective, we present the first O(n log(u/n))-bit dictionary structure which supports these queries in nearoptimal time under RAM model. We also build a dictionary which requires the same space and supports membership, select, and partial rank queries even more quickly in O(log log n) time. To the best of our knowledge, this is the first of a kind result which achieves data-aware space usage and retains near-optimal time. 1 Ankur Gupta http://works.bepress.com/ankur_gupta/3 http://works.bepress.com/ankur_gupta/3 Wed, 24 Feb 2010 06:36:35 PST A succinct data structure occupies an amount of space that is close to the information-theoretic minimum plus an additional term. The latter is not necessarily a lower-order term and, in several cases, completely dominates the space occupancy both in theory and in practice. In this paper, we present several solutions to partially overcome this problem, introducing new techniques of independent interest that allow us to improve over previously known upper and lower bounds. Alexander Golynski http://works.bepress.com/ankur_gupta/2 http://works.bepress.com/ankur_gupta/2 Wed, 24 Feb 2010 06:29:33 PST In this paper, we present a nearly tight analysis of the encoding length of the Burrows-Wheeler Transform (bwt) that is motivated by the text indexing setting. For a text T of n symbols drawn from an alphabet , our encoding scheme achieves bounds in terms of the hth-order empirical entropy Hh of the text, and takes linear time for encoding and decoding. We also describe a lower bound on the encoding length of the bwt that constructs an innite (non-trivial) class of texts that are among the hardest to compress using the bwt. We then show that our upper bound encoding length is nearly tight with this lower bound for the class of texts we described. In designing our bwt encoding and its lower bound, we also address the t-subset problem; here, the goal is to store a subset of t items drawn from a universe [1::n] using just lg 􀀀n t +O(1) bits of space. A number of solutions to this basic problem are known, however encoding or decoding usually requires either O(t) operations on large integers [Knu05, Rus05] or O(n) operations. We provide a novel approach to reduce the encoding/decoding time to just O(t) operations on small integers (of size O(lg n) bits), without increasing the space required. Roberto Grossi http://works.bepress.com/ankur_gupta/1 http://works.bepress.com/ankur_gupta/1 Sat, 26 Sep 2009 13:35:00 PDT Current data structures for searching large string collections either fail to achieve minimum space or cause too many cache misses. In this paper we discuss some edge linearizations of the classic trie data structure that are simultaneously cache-friendly and compressed. We provide new insights on front coding [24], introduce other novel linearizations, and study how close their space occupancy is to the information-theoretic minimum. The moral is that they are not just heuristics. Our second contribution is a novel dictionary encoding scheme that builds upon such linearizations and achieves nearly optimal space, offers competitive I/O-search time, and is also conscious of the query distribution. Finally, we combine those data structures with cache-oblivious tries [2, 5] and obtain a succinct variant whose space is close to the information-theoretic minimum. Ankur Gupta