| Title: | Graph theory approaches to maturity models : master thesis |
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| Authors: | ID Kajzer, Špela (Author)
ID Bokal, Drago (Mentor) More about this mentor... 
ID Nöllenburg, Martin (Comentor) |
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| Files: |  MAG_Kajzer_Spela_2024.pdf (1,46 MB)
MD5: 388C880501FE16BF252923122D8E1A4D
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| Language: | English |
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| Work type: | Master's thesis/paper |
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| Typology: | 2.09 - Master's Thesis |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | The masters thesis, which follows the paper Graph drawing applications in combinatorial theory of maturity models, in preparation, coauthored by the author of the thesis, introduces the tiled graphs as models of learning and maturing processes. In the thesis, we show how tiled graphs can combine graphs of learning spaces or antimatroids (partial cubes) and maturity models (total orders) to yield models of learning processes. We visualise processes with optimal drawings. In the thesis, we show NP-hardness of visualisation problems resulting from most detailed models. Further, we introduce a simpler model, which ignores the details of learning and for which the visualisation problem can be solved in a polynomial time. For the rest of the thesis, we consider this model. We describe an algorithm, which finds a drawing of an ordinal panel data graph with a minimal number of edge crossings. For this problem we further define an extremal crossing number for a chosen family of ordinal panel data. Further, we explore a certain type of random instances of ordinal panel data and the expected value of a crossing number for this type of random instances. After that, we define a problem of finding the most suitable ordering on categories in panel data, in other words finding the best maturity model to fit the data. We prove the NP-hardness of the problem and formulate an integer linear program.
Master thesis consists of nine chapters. The first chapter contains known results and definitions from set and graph theory and a section of computational complexity theory (NP-hardness), which will be used throughout the thesis. The following chapters present the new theory introduced in the aforementioned paper in preparation and the needed additional results and definitions. In the last chapter we present the thesis and some selected parts of the thesis with the help of learning space theory. The chapter serves as both the overview of the thesis and the use case for the theory of learning spaces, presented in the thesis. |
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| Keywords: | Maturity models, learning spaces, crossing number, crossing minimisation, tile crossing number. |
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| Place of publishing: | Maribor |
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| Place of performance: | Maribor |
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| Publisher: | Š. Kajzer |
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| Year of publishing: | 2024 |
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| Number of pages: | 114 str. |
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| PID: | 20.500.12556/DKUM-86779 |
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| UDC: | 519.17:519.85(043.2) |
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| COBISS.SI-ID: | 188712195 |
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| Publication date in DKUM: | 14.03.2024 |
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| Views: | 621 |
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| Downloads: | 66 |
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| Metadata: |    |
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| Categories: | FNM
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