The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Nathan Berkovits - One of the best experts on this subject based on the ideXlab platform.
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pure spinor formalism as an n 2 topological string
Journal of High Energy Physics, 2005Co-Authors: Nathan BerkovitsAbstract:Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the Superstring. Twisted ĉ = 3 N = 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop Superstring amplitudes without picture-changing operators, the construction of a cubic open Superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action.
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On the Worldsheet Derivation of Large N Dualities for the Superstring
Communications in Mathematical Physics, 2004Co-Authors: Nathan Berkovits, Hirosi Ooguri, Cumrun VafaAbstract:Large N topological string dualities have led to a class of proposed open/closed dualities for Superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional Superstring dualities by showing how the dualities arise on the Superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the Superstring is equivalent to a $\hat c=5$ topological string in ten-dimensional spacetime. Using the $\hat c=5$ description, we then show that the D brane boundary state for the ten-dimensional open Superstring naturally emerges on the worldsheet of the closed Superstring dual.
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ten dimensional supergravity constraints from the pure spinor formalism for the Superstring
Nuclear Physics, 2002Co-Authors: Nathan Berkovits, P S HoweAbstract:Abstract It has recently been shown that the ten-dimensional Superstring can be quantized using the BRST operator Q =∮ λ α d α , where λ α is a pure spinor satisfying λγ m λ =0 and d α is the fermionic supersymmetric derivative. In this paper, the pure spinor version of Superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the on-shell superspace constraints of the supergravity background. This is shown to lowest order in α ′ for the heterotic and Type II Superstrings, thus providing a compact pure spinor version of the ten-dimensional superspace constraints for N =1 Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the Superstring, it is expected that these methods can also be used to compute higher-order α ′ corrections to the ten-dimensional superspace constraints.
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Extra Dimensions in Superstring Theory
Nuclear Physics B, 1997Co-Authors: Nathan BerkovitsAbstract:It was earlier shown that an SO(9,1) $\theta^\a$ spinor variable can be constructed from RNS matter and ghost fields. $\theta^\a$ has a bosonic worldsheet super-partner $\lambda^\a$ which plays the role of a twistor variable, satisfying $\lambda\Gamma^\mu\lambda = \partial x^\mu +i\theta\Gamma^\mu \partial\theta$. For Type IIA Superstrings, the left-moving $[\theta_L^\a,\lambda_L^\a]$ and right-moving $[\theta_{R\a},\lambda_{R\a}]$ can be combined into 32-component SO(10,1) spinors $[\theta^A,\lambda^A]$. This suggests that $\lambda^A \Gamma^{11}_{AB}\lambda^B= 2\lambda_L^\a \lambda_{R\a}$ can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum vertex operators of the Type IIA Superstring and from consideration of $D_0$-branes. As in the work of Bars, one finds an SO(10,2) structure for the Type IIA Superstring and an SO(9,1) x SO(2,1) structure for the Type IIB Superstring.
P S Howe - One of the best experts on this subject based on the ideXlab platform.
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ten dimensional supergravity constraints from the pure spinor formalism for the Superstring
Nuclear Physics, 2002Co-Authors: Nathan Berkovits, P S HoweAbstract:Abstract It has recently been shown that the ten-dimensional Superstring can be quantized using the BRST operator Q =∮ λ α d α , where λ α is a pure spinor satisfying λγ m λ =0 and d α is the fermionic supersymmetric derivative. In this paper, the pure spinor version of Superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the on-shell superspace constraints of the supergravity background. This is shown to lowest order in α ′ for the heterotic and Type II Superstrings, thus providing a compact pure spinor version of the ten-dimensional superspace constraints for N =1 Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the Superstring, it is expected that these methods can also be used to compute higher-order α ′ corrections to the ten-dimensional superspace constraints.
Eric Rivals - One of the best experts on this subject based on the ideXlab platform.
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Greedy-reduction from Shortest Linear Superstring to Shortest Circular Superstring.
arXiv: Data Structures and Algorithms, 2020Co-Authors: Bastien Cazaux, Eric RivalsAbstract:A Superstring of a set of strings correspond to a string which contains all the other strings as substrings. The problem of finding the Shortest Linear Superstring is a well-know and well-studied problem in stringology. We present here a variant of this problem, the Shortest Circular Superstring problem where the sought Superstring is a circular string. We show a strong link between these two problems and prove that the Shortest Circular Superstring problem is NP-complete. Moreover, we propose a new conjecture on the approximation ratio of the Shortest Circular Superstring problem.
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Relationship between Superstring and compression measures: New insights on the greedy conjecture
Discrete Applied Mathematics, 2018Co-Authors: Bastien Cazaux, Eric RivalsAbstract:A Superstring of a set of words is a string that contains each input word as a substring. Given such a set, the Shortest Superstring Problem (SSP) asks for a Superstring of minimum length. SSP is an important theoretical problem related to the Asymmetric Travelling Salesman Problem, and also has practical applications in data compression and in bioinformatics. Indeed, it models the question of assembling a genome from a set of sequencing reads. Unfortunately, SSP is known to be NP-hard even on a binary alphabet and also hard to approximate with respect to the Superstring length or to the compression achieved by the Superstring. Even the variant in which all words share the same length r, called r-SSP, is NP-hard whenever r > 2. Numerous involved approximation algorithms achieve approximation ratio above 2 for the Superstring, but remain difficult to implement in practice. In contrast the greedy conjecture asked in 1988 whether a simple greedy algorithm achieves ratio of 2 for SSP. Here, we present a novel approach to bound the Superstring approximation ratio with the compression ratio, which, when applied to the greedy algorithm, shows a 2 approximation ratio for 3-SSP, and also that greedy achieves ratios smaller than 2. This leads to a new version of the greedy conjecture.
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CPM - Superstrings with multiplicities
2018Co-Authors: Bastien Cazaux, Eric RivalsAbstract:A Superstring of a set of words P = {s_1, ..., s_p } is a string that contains each word of P as substring. Given P, the well known Shortest Linear Superstring problem (SLS), asks for a shortest Superstring of P. In a variant of SLS, called Multi-SLS, each word s_i comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest Superstring that contains at least m(i) occurrences of s_i. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest Superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a Superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the Superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems.
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Superstrings with multiplicities
2018Co-Authors: Eric Rivals, Bastien CazauxAbstract:A Superstring of a set of words P = {s 1 ,. .. , s p } is a string that contains each word of P as substring. Given P , the well known Shortest Linear Superstring problem (SLS), asks for a shortest Superstring of P. In a variant of SLS, called Multi-SLS, each word s i comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest Superstring that contains at least m(i) occurrences of s i. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest Superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a Superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the Superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems.
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Practical lower and upper bounds for the Shortest Linear Superstring
2018Co-Authors: Bastien Cazaux, Samuel Juhel, Eric RivalsAbstract:Given a set P of words, the Shortest Linear Superstring (SLS) problem is an optimization problem that asks for a Superstring of $P$ of minimal length. SLS has applications in data compression, where a Superstring is a compact representation of $P$, and in bioinformatics where it models the first step of genome assembly. Unfortunately SLS is hard to solve (NP-hard) and to closely approximate (MAX-SNP-hard). If numerous polynomial time approximation algorithms have been devised, few articles report on their practical performance. We lack knowledge about how closely an approximate Superstring can be from an optimal one in practice. Here, we exhibit a linear time algorithm that reports an upper and a lower bound on the length of an optimal Superstring. The upper bound is the length of a Superstring. This algorithm can be used to evaluate beforehand whether one can get an approximate Superstring whose length is close to the optimum for a given instance. Experimental results suggest that its approximation performance is orders of magnitude better than previously reported practical values. Moreover, the proposed algorithm remain efficient even on large instances and can serve to explore in practice the approximability of SLS.
Bastien Cazaux - One of the best experts on this subject based on the ideXlab platform.
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Greedy-reduction from Shortest Linear Superstring to Shortest Circular Superstring.
arXiv: Data Structures and Algorithms, 2020Co-Authors: Bastien Cazaux, Eric RivalsAbstract:A Superstring of a set of strings correspond to a string which contains all the other strings as substrings. The problem of finding the Shortest Linear Superstring is a well-know and well-studied problem in stringology. We present here a variant of this problem, the Shortest Circular Superstring problem where the sought Superstring is a circular string. We show a strong link between these two problems and prove that the Shortest Circular Superstring problem is NP-complete. Moreover, we propose a new conjecture on the approximation ratio of the Shortest Circular Superstring problem.
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Relationship between Superstring and compression measures: New insights on the greedy conjecture
Discrete Applied Mathematics, 2018Co-Authors: Bastien Cazaux, Eric RivalsAbstract:A Superstring of a set of words is a string that contains each input word as a substring. Given such a set, the Shortest Superstring Problem (SSP) asks for a Superstring of minimum length. SSP is an important theoretical problem related to the Asymmetric Travelling Salesman Problem, and also has practical applications in data compression and in bioinformatics. Indeed, it models the question of assembling a genome from a set of sequencing reads. Unfortunately, SSP is known to be NP-hard even on a binary alphabet and also hard to approximate with respect to the Superstring length or to the compression achieved by the Superstring. Even the variant in which all words share the same length r, called r-SSP, is NP-hard whenever r > 2. Numerous involved approximation algorithms achieve approximation ratio above 2 for the Superstring, but remain difficult to implement in practice. In contrast the greedy conjecture asked in 1988 whether a simple greedy algorithm achieves ratio of 2 for SSP. Here, we present a novel approach to bound the Superstring approximation ratio with the compression ratio, which, when applied to the greedy algorithm, shows a 2 approximation ratio for 3-SSP, and also that greedy achieves ratios smaller than 2. This leads to a new version of the greedy conjecture.
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CPM - Superstrings with multiplicities
2018Co-Authors: Bastien Cazaux, Eric RivalsAbstract:A Superstring of a set of words P = {s_1, ..., s_p } is a string that contains each word of P as substring. Given P, the well known Shortest Linear Superstring problem (SLS), asks for a shortest Superstring of P. In a variant of SLS, called Multi-SLS, each word s_i comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest Superstring that contains at least m(i) occurrences of s_i. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest Superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a Superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the Superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems.
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Superstrings with multiplicities
2018Co-Authors: Eric Rivals, Bastien CazauxAbstract:A Superstring of a set of words P = {s 1 ,. .. , s p } is a string that contains each word of P as substring. Given P , the well known Shortest Linear Superstring problem (SLS), asks for a shortest Superstring of P. In a variant of SLS, called Multi-SLS, each word s i comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest Superstring that contains at least m(i) occurrences of s i. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest Superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a Superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the Superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems.
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Practical lower and upper bounds for the Shortest Linear Superstring
2018Co-Authors: Bastien Cazaux, Samuel Juhel, Eric RivalsAbstract:Given a set P of words, the Shortest Linear Superstring (SLS) problem is an optimization problem that asks for a Superstring of $P$ of minimal length. SLS has applications in data compression, where a Superstring is a compact representation of $P$, and in bioinformatics where it models the first step of genome assembly. Unfortunately SLS is hard to solve (NP-hard) and to closely approximate (MAX-SNP-hard). If numerous polynomial time approximation algorithms have been devised, few articles report on their practical performance. We lack knowledge about how closely an approximate Superstring can be from an optimal one in practice. Here, we exhibit a linear time algorithm that reports an upper and a lower bound on the length of an optimal Superstring. The upper bound is the length of a Superstring. This algorithm can be used to evaluate beforehand whether one can get an approximate Superstring whose length is close to the optimum for a given instance. Experimental results suggest that its approximation performance is orders of magnitude better than previously reported practical values. Moreover, the proposed algorithm remain efficient even on large instances and can serve to explore in practice the approximability of SLS.
Saket Saurabh - One of the best experts on this subject based on the ideXlab platform.
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Parameterized Complexity of Superstring Problems
Algorithmica, 2016Co-Authors: Ivan Bliznets, Fedor V. Fomin, Petr A. Golovach, Nikolay Karpov, Alexander S. Kulikov, Saket SaurabhAbstract:In the Shortest Superstring problem we are given a set of strings \(S=\{s_1, \ldots , s_n\}\) and an integer \(\ell \) and the question is to decide whether there is a Superstring \(s\) of length at most \(\ell \) containing all strings of \(S\) as substrings. We obtain several parameterized algorithms and complexity results for this problem.
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CPM - Parameterized Complexity of Superstring Problems
Combinatorial Pattern Matching, 2015Co-Authors: Ivan Bliznets, Fedor V. Fomin, Petr A. Golovach, Nikolay Karpov, Alexander S. Kulikov, Saket SaurabhAbstract:In the Shortest Superstring problem we are given a set of strings \(S=\{s_1, \ldots , s_n\}\) and an integer \(\ell \) and the question is to decide whether there is a Superstring \(s\) of length at most \(\ell \) containing all strings of \(S\) as substrings. We obtain several parameterized algorithms and complexity results for this problem.
