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Ganguly Arnab - One of the best experts on this subject based on the ideXlab platform.
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Structural Pattern Matching - Succinctly
LIPIcs - Leibniz International Proceedings in Informatics. 28th International Symposium on Algorithms and Computation (ISAAC 2017), 2017Co-Authors: Ganguly Arnab, Shah Rahul, Thankachan SharmaAbstract:Let T be a text of length n containing characters from an alphabet Sigma, which is the union of two disjoint sets: Sigma_s containing static characters (s-characters) and Sigma_p containing parameterized characters (p-characters). Each character in Sigma_p has an associated complementary character from Sigma_p. A pattern P (also over Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a One-to-One Function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y. The task is to find the starting positions (occurrences) of all such substrings S. Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires Theta(nlog n) bits of space, and can find all occ occurrences in time O(|P|log sigma+ occ), where sigma = |Sigma|. In this paper, we present the first succinct index for this problem, which occupies n log sigma + O(n) bits and offers O(|P|logsigma+ occcdot log n logsigma) query time
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Succinct Data Structures for Parameterized Pattern Matching and Related Problems
LSU Digital Commons, 2017Co-Authors: Ganguly ArnabAbstract:Let T be a fixed text-string of length n and P be a varying pattern-string of length |P| \u3c= n. Both T and P contain characters from a totally ordered alphabet Sigma of size sigma \u3c= n. Suffix tree is the ubiquitous data structure for answering a pattern matching query: report all the positions i in T such that T[i + k - 1] = P[k], 1 \u3c= k \u3c= |P|. Compressed data structures support pattern matching queries, using much lesser space than the suffix tree, mainly by relying on a crucial property of the leaves in the tree. Unfortunately, in many suffix tree variants (such as parameterized suffix tree, order-preserving suffix tree, and 2-dimensional suffix tree), this property does not hold. Consequently, compressed representations of these suffix tree variants have been elusive. We present the first compressed data structures for two important variants of the pattern matching problem: (1) Parameterized Matching -- report a position i in T if T[i + k - 1] = f(P[k]), 1 \u3c= k \u3c= |P|, for a One-to-One Function f that renames the characters in P to the characters in T[i,i+|P|-1], and (2) Order-preserving Matching -- report a position i in T if T[i + j - 1] and T[i + k -1] have the same relative order as that of P[j] and P[k], 1 \u3c= j \u3c k \u3c= |P|. For each of these two problems, the existing suffix tree variant requires O(n*log n) bits of space and answers a query in O(|P|*log sigma + occ) time, where occ is the number of starting positions where a match exists. We present data structures that require O(n*log sigma) bits of space and answer a query in O((|P|+occ) poly(log n)) time. As a byproduct, we obtain compressed data structures for a few other variants, as well as introduce two new techniques (of independent interest) for designing compressed data structures for pattern matching
Thankachan Sharma - One of the best experts on this subject based on the ideXlab platform.
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Structural Pattern Matching - Succinctly
LIPIcs - Leibniz International Proceedings in Informatics. 28th International Symposium on Algorithms and Computation (ISAAC 2017), 2017Co-Authors: Ganguly Arnab, Shah Rahul, Thankachan SharmaAbstract:Let T be a text of length n containing characters from an alphabet Sigma, which is the union of two disjoint sets: Sigma_s containing static characters (s-characters) and Sigma_p containing parameterized characters (p-characters). Each character in Sigma_p has an associated complementary character from Sigma_p. A pattern P (also over Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a One-to-One Function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y. The task is to find the starting positions (occurrences) of all such substrings S. Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires Theta(nlog n) bits of space, and can find all occ occurrences in time O(|P|log sigma+ occ), where sigma = |Sigma|. In this paper, we present the first succinct index for this problem, which occupies n log sigma + O(n) bits and offers O(|P|logsigma+ occcdot log n logsigma) query time
Shah Rahul - One of the best experts on this subject based on the ideXlab platform.
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Structural Pattern Matching - Succinctly
LIPIcs - Leibniz International Proceedings in Informatics. 28th International Symposium on Algorithms and Computation (ISAAC 2017), 2017Co-Authors: Ganguly Arnab, Shah Rahul, Thankachan SharmaAbstract:Let T be a text of length n containing characters from an alphabet Sigma, which is the union of two disjoint sets: Sigma_s containing static characters (s-characters) and Sigma_p containing parameterized characters (p-characters). Each character in Sigma_p has an associated complementary character from Sigma_p. A pattern P (also over Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a One-to-One Function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y. The task is to find the starting positions (occurrences) of all such substrings S. Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires Theta(nlog n) bits of space, and can find all occ occurrences in time O(|P|log sigma+ occ), where sigma = |Sigma|. In this paper, we present the first succinct index for this problem, which occupies n log sigma + O(n) bits and offers O(|P|logsigma+ occcdot log n logsigma) query time
John Asher Johnson - One of the best experts on this subject based on the ideXlab platform.
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retired a stars revisited an updated giant planet occurrence rate as a Function of stellar metallicity and mass
arXiv: Solar and Stellar Astrophysics, 2018Co-Authors: Luan Ghezzi, Benjamin T Montet, John Asher JohnsonAbstract:Exoplanet surveys of evolved stars have provided increasing evidence that the formation of giant planets depends not only on stellar metallicity ([Fe/H]), but also the mass ($M_\star$). However, measuring accurate masses for subgiants and giants is far more challenging than it is for their main-sequence counterparts, which has led to recent concerns regarding the veracity of the correlation between stellar mass and planet occurrence. In order to address these concerns we use HIRES spectra to perform a spectroscopic analysis on an sample of 245 subgiants and derive new atmospheric and physical parameters. We also calculate the space velocities of this sample in a homogeneous manner for the first time. When reddening corrections are considered in the calculations of stellar masses and a -0.12 M$_{\odot}$ offset is applied to the results, the masses of the subgiants are consistent with their space velocity distributions, contrary to claims in the literature. Similarly, our measurements of their rotational velocities provide additional confirmation that the masses of subgiants with $M_\star \geq 1.6$ M$_{\odot}$ (the "Retired A Stars") have not been overestimated in previous analyses. Using these new results for our sample of evolved stars, together with an updated sample of FGKM dwarfs, we confirm that giant planet occurrence increases with both stellar mass and metallicity up to 2.0 M$_{\odot}$. We show that the probability of formation of a giant planet is approximately a One-to-One Function of the total amount of metals in the protoplanetary disk $M_\star 10^{[Fe/H]}$. This correlation provides additional support for the core accretion mechanism of planet formation.
Sharma V Thankachan - One of the best experts on this subject based on the ideXlab platform.
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parameterized text indexing with one wildcard
Data Compression Conference, 2019Co-Authors: Arnab Ganguly, Yuan Huang, Solon P Pissis, Rahul Shah, Sharma V ThankachanAbstract:Two equal-length strings X and Y over an alphabet Σ of size σ are a parameterized match iff X can be transformed to Y by renaming the character X[i] to the character Y[i] for 1 ≤ i ≤ |X| using a One-to-One Function from the set of characters in X to the set of characters in Y. The parameterized text indexing problem is defined as: Index a text T of n characters over an alphabet set Σ of size σ, such that whenever a pattern P[1, p] comes as a query, we can report all occ parameterized occurrences of P in T. A position i ∊ [1, n] is a parameterized occurrence of P in T, iff P and T[i,(i+p-1)] are a parameterized match. We study an interesting generalization of this problem, where the pattern contains one wildcard character ϕ ∉ Σ that matches with any other character in Σ. Therefore, for a pattern P[1, p] = P_1ϕP_2, our task is to report all positions i in T, such that the string P_1 P_2 and the string obtained by concatenating T[i,(i+|P_1|-1)] and T[(i+|P_1|+1),(i+p-1)] are a parameterized match. We show that such queries can be answered in optimal O(p+occ) time per query using an O(n log n) space index. We then show how to compress our index into O(n log σ) space but with a higher query cost of O(p(log log n+logσ)+occ logσ).
