Simplifying the beamforming optimality region for practical mimo scenarios

Matilde Sanchez-Fernandez; Santiago Zazo; Reinaldo Valenzuela

doi:10.1109/lcomm.2006.060911

Simplifying the beamforming optimality region for practical mimo scenarios

IEEE Communications Letters ◽

10.1109/lcomm.2006.060911 ◽

2006 ◽

Vol 10 (11) ◽

pp. 751-753 ◽

Cited By ~ 1

Author(s):

Matilde Sanchez-Fernandez ◽

Santiago Zazo ◽

Reinaldo Valenzuela

Keyword(s):

Optimality Region

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Optimality Region for Job Permutation in Single-Machine Scheduling with Uncertain Processing Times

Automation and Remote Control ◽

10.1134/s0005117920050045 ◽

2020 ◽

Vol 81 (5) ◽

pp. 819-842

Author(s):

Yu. N. Sotskov

Keyword(s):

Single Machine ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Processing Times ◽

Optimality Region

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The Optimality Region for a Single-Machine Scheduling Problem with Bounded Durations of the Jobs and the Total Completion Time Objective

Mathematics ◽

10.3390/math7050382 ◽

2019 ◽

Vol 7 (5) ◽

pp. 382 ◽

Cited By ~ 3

Author(s):

Yuri N. Sotskov ◽

Natalja G. Egorova

Keyword(s):

Single Machine ◽

Completion Time ◽

Optimal Schedule ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Total Completion Time ◽

Scheduling Problem ◽

Lower And Upper Bounds ◽

The Given ◽

Optimality Region

We study a single-machine scheduling problem to minimize the total completion time of the given set of jobs, which have to be processed without job preemptions. The lower and upper bounds on the job duration is the only information that is available before scheduling. Exact values of the job durations remain unknown until the completion of the jobs. We use the optimality region for the job permutation as an optimality measure of the optimal schedule. We investigate properties of the optimality region and derive O ( n ) -algorithm for calculating a quasi-perimeter of the optimality set (i.e., the sum of lengths of the optimality segments for n given jobs). We develop a fast algorithm for finding a job permutation having the largest quasi-perimeter of the optimality set. The computational results in constructing such permutations show that they are close to the optimal ones, which can be constructed for the factual durations of all given jobs.

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