A LOW OVERHEAD SCHEDULE FOR A 3D-GRID GRAPH

1992 ◽  
Vol 02 (04) ◽  
pp. 363-372 ◽  
Author(s):  
E. BAMPIS ◽  
J.-C. KÖNIG ◽  
D. TRYSTRAM
Keyword(s):  
Lower Bound ◽  
Scheduling Algorithm ◽  
Three Dimensional ◽  
Fixed Number ◽  
Communication Overhead ◽  
Grid Graph ◽  
Precedence Graph

We propose a new scheduling algorithm for a three-dimensional grid precedence graph of size n, and we prove that the communication overhead is just in Θ( log log n). Finally, we show that a lower bound for the overhead of any schedule with a fixed number of processors (p ≥ 3) is Ω( log log n).

ONLINE SCHEDULING OF DYNAMIC TREES

1995 ◽  
Vol 05 (04) ◽  
pp. 635-646 ◽  
Author(s):  
MICHAEL A. PALIS ◽  
JING-CHIOU LIOU ◽  
SANGUTHEVAR RAJASEKARAN ◽  
SUNIL SHENDE ◽  
DAVID S.L. WEI
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Scheduling Algorithm ◽  
Optimal Schedule ◽  
Online Scheduling ◽  
The Other ◽  
Static Case ◽  
Scheduling Problem ◽  
Dynamic Trees ◽  
Dynamic Tree

The scheduling problem for dynamic tree-structured task graphs is studied and is shown to be inherently more difficult than the static case. It is shown that any online scheduling algorithm, deterministic or randomized, has competitive ratio Ω((1/g)/ log d(1/g)) for trees with granularity g and degree at most d. On the other hand, it is known that static trees with arbitrary granularity can be scheduled to within twice the optimal schedule. It is also shown that the lower bound is tight: there is a deterministic online tree scheduling algorithm that has competitive ratio O((1/g)/ log d(1/g)). Thus, randomization does not help.

scholarly journals Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings

2005 ◽  
Vol 177 ◽  
pp. 47-75 ◽  
Author(s):  
Kei-ichi Watanabe ◽  
Ken-ichi Yoshida
Keyword(s):  
Lower Bound ◽  
Local Ring ◽  
Three Dimensional ◽  
Krull Dimension ◽  
Local Rings ◽  
Mild Conditions ◽  
Quadric Hypersurface ◽  
Complete Local Ring

In this paper, we investigate the lower bound sHK(p, d) of Hilbert-Kunz multiplicities for non-regular unmixed local rings of Krull dimension d containing a field of characteristic p > 0. Especially, we focus on three-dimensional local rings. In fact, as a main result, we will prove that sHK (p, 3) = 4/3 and that a three-dimensional complete local ring of Hilbert-Kunz multiplicity 4/3 is isomorphic to the non-degenerate quadric hypersurface k[[X, Y, Z,W]]/(X2 + Y2 + Z2 + W2) under mild conditions.Furthermore, we pose a generalization of the main theorem to the case of dim A ≥ 4 as a conjecture, and show that it is also true in case dim A = 4 using the similar method as in the proof of the main theorem.

TIME LOWER BOUNDS FOR PERMUTATION ROUTING ON MULTI-DIMENSIONAL BUSED MESHES

1993 ◽  
Vol 03 (02) ◽  
pp. 129-138
Author(s):  
STEVEN CHEUNG ◽  
FRANCIS C.M. LAU
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Routing Problem ◽  
Higher Dimensional ◽  
Low Dimensional ◽  
Permutation Routing

We present time lower bounds for the permutation routing problem on three- and higher-dimensional n x…x n meshes with buses. We prove an (r–1)n/r lower bound for the general case of an r-dimensional bused mesh, r≥2, which is not as strong for low-dimensional as for higher-dimensional cases. We then use a different approach to construct a 0.705n lower bound for the three-dimensional case.

Study of parallel programming models on computer clusters with Intel MIC coprocessors

2015 ◽  
Vol 31 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Miaoqing Huang ◽  
Chenggang Lai ◽  
Xuan Shi ◽  
Zhijun Hao ◽  
Haihang You
Keyword(s):  
Parallel Programming ◽  
High Performance ◽  
Programming Model ◽  
Fixed Number ◽  
Parallel Applications ◽  
Programming Models ◽  
Communication Overhead ◽  
Computer Clusters ◽  
Parallel Programming Models ◽  
Intel Mic

Coprocessors based on the Intel Many Integrated Core (MIC) Architecture have been adopted in many high-performance computer clusters. Typical parallel programming models, such as MPI and OpenMP, are supported on MIC processors to achieve the parallelism. In this work, we conduct a detailed study on the performance and scalability of the MIC processors under different programming models using the Beacon computer cluster. Our findings are as follows. (1) The native MPI programming model on the MIC processors is typically better than the offload programming model, which offloads the workload to MIC cores using OpenMP. (2) On top of the native MPI programming model, multithreading inside each MPI process can further improve the performance for parallel applications on computer clusters with MIC coprocessors. (3) Given a fixed number of MPI processes, it is a good strategy to schedule these MPI processes to as few MIC processors as possible to reduce the cross-processor communication overhead. (4) The hybrid MPI programming model, in which data processing is distributed to both MIC cores and CPU cores, can outperform the native MPI programming model.

SIMULATIONS BY TIME-BOUNDED COUNTER MACHINES

2011 ◽  
Vol 22 (02) ◽  
pp. 395-409 ◽  
Author(s):  
HOLGER PETERSEN
Keyword(s):  
Lower Bound ◽  
Real Time ◽  
Polynomial Time ◽  
Time Complexity ◽  
Linear Time ◽  
Fixed Number ◽  
Exponential Time ◽  
New Family ◽  
Counter Machines ◽  
Time Bounds

We investigate the efficiency of simulations of storages by several counters. A simulation of a pushdown store is described which is optimal in the sense that reducing the number of counters of a simulator leads to an increase in time complexity. The lower bound also establishes a tight counter hierarchy in exponential time. Then we turn to simulations of a set of counters by a different number of counters. We improve and generalize a known simulation in polynomial time. Greibach has shown that adding s + 1 counters increases the power of machines working in time ns. Using a new family of languages we show here a tight hierarchy result for machines with the same polynomial time-bound. We also prove hierarchies for machines with a fixed number of counters and with growing polynomial time-bounds. For machines with one counter and an additional "store zero" instruction we establish the equivalence of real-time and linear time. If at least two counters are available, the classes of languages accepted in real-time and linear time can be separated.

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