scholarly journals Quantum and Classical Strong Direct Product Theorems and Optimal Time‐Space Tradeoffs

2007 ◽  
Vol 36 (5) ◽  
pp. 1472-1493 ◽  
Author(s):  
Hartmut Klauck ◽  
Robert Špalek ◽  
Ronald de Wolf
Keyword(s):  
Direct Product ◽  
Optimal Time ◽  
Time Space ◽  
Direct Product Theorems

scholarly journals A New Quantum Lower Bound Method, with Applications to Direct Product Theorems and Time-Space Tradeoffs

Algorithmica ◽  
2007 ◽  
Vol 55 (3) ◽  
pp. 422-461 ◽  
Author(s):  
Andris Ambainis ◽  
Robert Špalek ◽  
Ronald de Wolf
Keyword(s):  
Lower Bound ◽  
Direct Product ◽  
Time Space ◽  
Direct Product Theorems

scholarly journals Chernoff-Type Direct Product Theorems

2007 ◽  
pp. 500-516 ◽  
Author(s):  
Russell Impagliazzo ◽  
Ragesh Jaiswal ◽  
Valentine Kabanets
Keyword(s):  
Direct Product ◽  
Direct Product Theorems

scholarly journals Optimal Time-Space Trade-Offs for Sorting

1998 ◽  
Vol 5 (10) ◽  
Author(s):  
Jakob Pagter ◽  
Theis Rauhe
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Fundamental Problem ◽  
Full Range ◽  
Optimal Time ◽  
Sorting Algorithm ◽  
Logarithmic Factor ◽  
Time Space ◽  
Trade Offs ◽  
Space Product

We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.<br />Beame has shown a lower bound of  Omega(n^2) for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of O(n^2 log n) due to Frederickson. Since then, no progress has been made towards tightening this gap.<br />The main contribution of this paper is a comparison based sorting algorithm which closes this gap by meeting the lower bound of Beame. The time-space product O(n^2) upper bound holds for the full range of space bounds between log n and n/log n. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame.

Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T17-T40 ◽  
Author(s):  
Zhiming Ren ◽  
Yang Liu
Keyword(s):  
Finite Difference ◽  
Stability Condition ◽  
Computational Cost ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Equation Modeling ◽  
Optimal Time ◽  
Finite Difference Schemes ◽  
Space Domain ◽  
Time Space

Staggered-grid finite-difference (SFD) methods are widely used in modeling seismic-wave propagation, and the coefficients of finite-difference (FD) operators can be estimated by minimizing dispersion errors using Taylor-series expansion (TE) or optimization. We developed novel optimal time-space-domain SFD schemes for acoustic- and elastic-wave-equation modeling. In our schemes, a fourth-order multiextreme value objective function with respect to FD coefficients was involved. To yield the globally optimal solution with low computational cost, we first used variable substitution to turn our optimization problem into a quadratic convex one and then used least-squares (LS) to derive the optimal SFD coefficients by minimizing the relative error of time-space-domain dispersion relations over a given frequency range. To ensure the robustness of our schemes, a constraint condition was imposed that the dispersion error at each frequency point did not exceed a given threshold. Moreover, the hybrid absorbing boundary condition was applied to remove artificial boundary reflections. We compared our optimal SFD with the conventional, TE-based time-space-domain, and LS-based SFD schemes. Dispersion analysis and numerical simulation results suggested that the new SFD schemes had a smaller numerical dispersion than the other three schemes when the same operator lengths were adopted. In addition, our LS-based time-space-domain SFD can obtain the same modeling accuracy with shorter spatial operator lengths. We also derived the stability condition of our schemes. The experiment results revealed that our new LS-based SFD schemes needed a slightly stricter stability condition.

Near-Optimal Time-Space Tradeoff for Element Distinctness

1994 ◽  
Vol 23 (5) ◽  
pp. 966-975 ◽  
Author(s):  
Andrew Chi-Chih Yao
Keyword(s):  
Optimal Time ◽  
Time Space

Chernoff-Type Direct Product Theorems

2008 ◽  
Vol 22 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Russell Impagliazzo ◽  
Ragesh Jaiswal ◽  
Valentine Kabanets
Keyword(s):  
Direct Product ◽  
Direct Product Theorems
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