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Algebraic Algorithms for LWE Problems
"... Abstract. We analyse the complexity of algebraic algorithms for solving systems of linear equations with noise. Such systems arise naturally in the theory of errorcorrecting codes as well as in computational learning theory. More recently, linear systems with noise have found application in cryptog ..."
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of Gröbner bases yields an exponential speedup over the basic AroraGe approach. On the other hand, we give a negative answer to the natural question whether the use of such techniques can yield a subexponential algorithm for the LWE problem. Under a mild algebraic assumption, we show that it is highly
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
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Cited by 776 (23 self)
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We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 638 (1 self)
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In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 1105 (20 self)
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.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing averageconsensus problems. We introduce disagreement functions that play the role of Lyapunov functions
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
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Cited by 862 (10 self)
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in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A 5dimensional depiction is developed, which completely describes the system. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
, 2007
"... Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An ove ..."
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Cited by 801 (3 self)
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. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems
On the Complexity of the BKW Algorithm on LWE
"... Abstract. In this paper we present a study of the complexity of the BlumKalaiWasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and computational effort requirements for solving concrete instances of the LWE problem. We app ..."
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Cited by 3 (0 self)
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Abstract. In this paper we present a study of the complexity of the BlumKalaiWasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and computational effort requirements for solving concrete instances of the LWE problem. We
Data Exchange: Semantics and Query Answering
 In ICDT
, 2003
"... Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to query answe ..."
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Cited by 425 (41 self)
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Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to query
A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 348 (11 self)
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Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had
RingLWE in polynomial rings
 In Public Key Cryptography
, 2012
"... Abstract. The RingLWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the RingLWE problem defined in [LPR10] involves the fractional ideal R ∨ , the dual of the ring R, which is the source ..."
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Cited by 6 (0 self)
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Abstract. The RingLWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the RingLWE problem defined in [LPR10] involves the fractional ideal R ∨ , the dual of the ring R, which is the source
Results 1  10
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