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Mixed Graph Colouring as Scheduling a Partially Ordered Set of Interruptible Multi-Processor Tasks with Integer Due Dates
by
Evangelina I. Mihova
Evangelina I. Mihova
Evangelina I. Mihova has been a student of the Mathematical Faculty at the Ludwig Maximilian in two [...]
Evangelina I. Mihova has been a student of the Mathematical Faculty at the Ludwig Maximilian University in Munch (Germany) since 2023. She published two papers as a co-author. Her current research topics include scheduling theory, production planning, graph theory and time management.
1 and
Yuri N. Sotskov
Yuri N. Sotskov
Yuri N. Sotskov, Prof.
D.Sc., finished secondary school with a gold medal in 1966 and the Faculty a [...]
Yuri N. Sotskov, Prof.
D.Sc., finished secondary school with a gold medal in 1966 and graduated
from the Faculty of Applied Mathematics of the Belarusian
State University
in Minsk in 1971. In 1980, he defended
his PhD thesis at the
Institute of Mathematics
of the National Academy of Sciences of Belarus
in Minsk. In
1991, he defended his D.Sc. thesis at the Institute
of Cybernetics of the National Academy
of Sciences of Ukraine in Kiev. He has the title of
Professor in Application of Mathematical Models and Methods in Scientific
Research (Russian Academy of Sciences, 1994). He currently works as a principal
researcher at the United Institute of Informatics Problems of the National
Academy of Sciences of Belarus
in Minsk. He
has more than 350 publications: five scientific monographs, two text books,
and more than 200 papers in international journals, books, and conference
proceedings in English on applied mathematics, operations research graph
theory and scheduling. He is on the Editorial Board of five journals. He has been
a supervisor of eight PhD scholars (defended). In 1998, he received the
National Prize of Belarus in Science and Engineering.
2,*
1
Mathematical Institute, Faculty of Mathematics, Computer Science and Statistics, Ludwig-Maximilians-Universitat Munich, Geschwister-Scholl-Platz, 1, 80539 Munich, Germany
2
United Institute of Informatics Problems, National Academy of Sciences, 6 Surganov Street, 220012 Minsk, Belarus
*
Author to whom correspondence should be addressed.
Algorithms 2024, 17(7), 299; https://doi.org/10.3390/a17070299 (registering DOI)
Submission received: 16 May 2024
/
Revised: 20 June 2024
/
Accepted: 1 July 2024
/
Published: 6 July 2024
Abstract
We investigate relationships between scheduling problems with the bottleneck objective functions (minimising makespan or maximal lateness) and problems of optimal colourings of the mixed graphs. The investigated scheduling problems have integer durations of the multi-processor tasks (operations), integer release dates and integer due dates of the given jobs. In the studied scheduling problems, it is required to find an optimal schedule for processing the partially ordered operations, given that operation interruptions are allowed and indicated subsets of the unit-time operations must be processed simultaneously. First, we show that the input data for any considered scheduling problem can be completely determined by the corresponding mixed graph. Second, we prove that solvable scheduling problems can be reduced to problems of finding optimal colourings of corresponding mixed graphs. Third, finding an optimal colouring of the mixed graph is equivalent to the considered scheduling problem determined by the same mixed graph. Finally, due to the proven equivalence of the considered optimisation problems, most of the results that were proven for the optimal colourings of mixed graphs generate similar results for considered scheduling problems, and vice versa.
Share and Cite
MDPI and ACS Style
Mihova, E.I.; Sotskov, Y.N.
Mixed Graph Colouring as Scheduling a Partially Ordered Set of Interruptible Multi-Processor Tasks with Integer Due Dates. Algorithms 2024, 17, 299.
https://doi.org/10.3390/a17070299
AMA Style
Mihova EI, Sotskov YN.
Mixed Graph Colouring as Scheduling a Partially Ordered Set of Interruptible Multi-Processor Tasks with Integer Due Dates. Algorithms. 2024; 17(7):299.
https://doi.org/10.3390/a17070299
Chicago/Turabian Style
Mihova, Evangelina I., and Yuri N. Sotskov.
2024. "Mixed Graph Colouring as Scheduling a Partially Ordered Set of Interruptible Multi-Processor Tasks with Integer Due Dates" Algorithms 17, no. 7: 299.
https://doi.org/10.3390/a17070299
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