Improved optimal algorithms for scheduling unit-length independent tasks on uniform machines

1994 ◽  
Vol 25 (3) ◽  
pp. 591-601 ◽  
Author(s):  
ALEKOS TRIANTAFYLLAKIS ◽  
SPYROS TZAFESTAS
Keyword(s):  
Unit Length ◽  
Optimal Algorithms ◽  
Uniform Machines ◽  
Independent Tasks

Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes

2015 ◽  
Vol 32 (05) ◽  
pp. 1550032 ◽  
Author(s):  
Xinrong Lu ◽  
Zhaohui Liu
Keyword(s):  
Speed Ratio ◽  
Scheduling Problem ◽  
Optimal Algorithms ◽  
Hierarchical Scheduling ◽  
Uniform Machines

This paper studies the online hierarchical scheduling problem on two uniform machines with bounded job sizes, where the first machine M1 receives both low and high hierarchy jobs, while the second machine M2 only receives high hierarchy jobs. The machines have a speed ratio of s(s ≥ 1), and M2 runs faster. Jobs are revealed one by one, and before the current job is scheduled, we have no information about next jobs except that the size of any job is in the interval [1, t]. The objective is to minimize the makespan. We present optimal algorithms for all (s, t) pairs.

scholarly journals Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines

2017 ◽  
Vol 65 (1) ◽  
pp. 29-34 ◽  
Author(s):  
H. Furmańczyk ◽  
M. Kubale
Keyword(s):  
Approximation Algorithm ◽  
General Problem ◽  
Unit Length ◽  
Mutual Exclusion ◽  
Np Hard ◽  
Uniform Machines ◽  
Identical Jobs ◽  
Incompatibility Graph

Abstract In the paper we consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s1 ≥ s2 ≥ s3 ≥ s4, respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree Δ, where two incompatible jobs cannot be processed on the same machine. We show that the general problem is NP-hard even if s1 = s2 = s3. If, however, Δ ≤ 4 and s1 ≥ 12s2, s2 = s3 = s4, then the problem can be solved to optimality in time O(n1.5). The same algorithm returns a solution of value at most 2 times optimal provided that s1 ≥ 2s2. Finally, we study the case s1 ≥ s2 ≥ s3 = s4 and give a 32/15-approximation algorithm running also in O(n1.5) time.

Scheduling of unit-length independent tasks with execution constraints

1976 ◽  
Vol 4 (4) ◽  
pp. 95-98 ◽  
Author(s):  
Tomás Lang ◽  
Eduardo B. Fernández
Keyword(s):  
Unit Length ◽  
Independent Tasks

Metallurgical Effects of Grain Boundary Ledges

1977 ◽  
Vol 35 ◽  
pp. 126-129
Author(s):  
L.E. Murr
Keyword(s):  
Grain Boundary ◽  
Quantitative Data ◽  
Mechanical Treatment ◽  
Unit Length ◽  
Physical And Mechanical Properties ◽  
Direct Observations ◽  
Transmission Electron ◽  
Properties Of Materials ◽  
Thermo Mechanical Treatment ◽  
Ledge Density

Ledges in grain boundaries can be identified by their characteristic contrast features (straight, black-white lines) distinct from those of lattice dislocations, for example1,2 [see Fig. 1(a) and (b)]. Simple contrast rules as pointed out by Murr and Venkatesh2, can be established so that ledges may be recognized with come confidence, and the number of ledges per unit length of grain boundary (referred to as the ledge density, m) measured by direct observations in the transmission electron microscope. Such measurements can then give rise to quantitative data which can be used to provide evidence for the influence of ledges on the physical and mechanical properties of materials.It has been shown that ledge density can be systematically altered in some metals by thermo-mechanical treatment3,4.

Characterization of microtubules by dark-field STEM and replication

1991 ◽  
Vol 49 ◽  
pp. 152-153
Author(s):  
S.B. Andrews ◽  
R.D. Leapman ◽  
P.E. Gallant ◽  
T.S. Reese
Keyword(s):  
Protein Interactions ◽  
Low Dose ◽  
Unit Length ◽  
Dark Field ◽  
Carbon Films ◽  
Microtubule Associated Proteins ◽  
Molecular Weights ◽  
Freeze Dried ◽  
Protein Motors ◽  
Associated Proteins

As part of a study on protein interactions involved in microtubule (MT)-based transport, we used the VG HB501 field-emission STEM to obtain low-dose dark-field mass maps of isolated, taxol-stabilized MTs and correlated these micrographs with detailed stereo images from replicas of the same MTs. This approach promises to be useful for determining how protein motors interact with MTs. MTs prepared from bovine and squid brain tubulin were purified and free from microtubule-associated proteins (MAPs). These MTs (0.1-1 mg/ml tubulin) were adsorbed to 3-nm evaporated carbon films supported over Formvar nets on 600-m copper grids. Following adsorption, the grids were washed twice in buffer and then in either distilled water or in isotonic or hypotonic ammonium acetate, blotted, and plunge-frozen in ethane/propane cryogen (ca. -185 C). After cryotransfer into the STEM, specimens were freeze-dried and recooled to ca.-160 C for low-dose (<3000 e/nm2) dark-field mapping. The molecular weights per unit length of MT were determined relative to tobacco mosaic virus standards from elastic scattering intensities. Parallel grids were freeze-dried and rotary shadowed with Pt/C at 14°.

Task Scheduling Algorithm based on Resources Segregation in Cloud Environment

2018 ◽  
pp. 96-101
Author(s):  
Shailendra Raghuvanshi ◽  
Priyanka Dubey
Keyword(s):  
Load Balancing ◽  
Task Scheduling ◽  
Waiting Time ◽  
Virtual Machines ◽  
Scheduling Algorithm ◽  
Cloud Environment ◽  
Task Scheduling Algorithm ◽  
Machine Utilization ◽  
Independent Tasks ◽  
Optimal Machine

Load balancing of non-preemptive independent tasks on virtual machines (VMs) is an important aspect of task scheduling in clouds. Whenever certain VMs are overloaded and remaining VMs are under loaded with tasks for processing, the load has to be balanced to achieve optimal machine utilization. In this paper, we propose an algorithm named honey bee behavior inspired load balancing, which aims to achieve well balanced load across virtual machines for maximizing the throughput. The proposed algorithm also balances the priorities of tasks on the machines in such a way that the amount of waiting time of the tasks in the queue is minimal. We have compared the proposed algorithm with existing load balancing and scheduling algorithms. The experimental results show that the algorithm is effective when compared with existing algorithms. Our approach illustrates that there is a significant improvement in average execution time and reduction in waiting time of tasks on queue using workflowsim simulator in JAVA.

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