Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order
It is increasingly common to find real-life structures or behaviors represented as graphs in many areas of the computing sciences. Comparing these graphs is a hard task, especially when we are interested in assigning a non-binary similarity score between two large graphs based on some domain-specifi...
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ftrit:oai:scholarworks.rit.edu:theses-11050 2023-07-02T03:33:24+02:00 Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order Nunez, Wilberto Z 2018-08-22T07:00:00Z application/pdf https://scholarworks.rit.edu/theses/9892 https://scholarworks.rit.edu/context/theses/article/11050/viewcontent/WNunezPichardoThesis8_22_2018.pdf unknown RIT Scholar Works https://scholarworks.rit.edu/theses/9892 https://scholarworks.rit.edu/context/theses/article/11050/viewcontent/WNunezPichardoThesis8_22_2018.pdf Theses Graph alignment Graphlet degree vector Induced subgraph Orbit count text 2018 ftrit 2023-06-13T18:39:56Z It is increasingly common to find real-life structures or behaviors represented as graphs in many areas of the computing sciences. Comparing these graphs is a hard task, especially when we are interested in assigning a non-binary similarity score between two large graphs based on some domain-specific context. In bioinformatics, social network analysis and other areas is frequently necessary to compute graph similarities based on the local topological information of each vertex of the given graphs. This is why graphlet degree vectors have become more and more popular in these areas. They provide a simple yet detailed representation of a vertex's topology by counting the number of times such vertex touches a list of small predefined sub-structures called graphlets. In this thesis, we study the state-of-the-art algorithm to compute graphlet degree vectors, the Orbit Counting Algorithm (ORCA). ORCA generates a triangular system of linear equations that can be quickly solved to obtain the graphlet degree vector of a vertex. We make theoretical and practical improvements to this algorithm and measure the difference in speed after these improvements. The theoretical improvement consists of finding automorphisms of graphlets given a fixed vertex that is required to map to itself in such automorphisms. We observe that one piece of the algorithm runs much faster than before with this improvement, especially for larger graphlet orders. This helps the algorithm take less time in generating the linear system that we use to find the desired graphlet degree vector. The practical improvement consists of making a flexible implementation of the algorithm, which can take any graphlet size as input, any number of input graphs, and compute the graphlet degree vector for every vertex in each one of those graphs. Text Orca Rochester Institute of Technology: RIT Scholar Works |
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Rochester Institute of Technology: RIT Scholar Works |
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Graph alignment Graphlet degree vector Induced subgraph Orbit count |
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Graph alignment Graphlet degree vector Induced subgraph Orbit count Nunez, Wilberto Z Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order |
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Graph alignment Graphlet degree vector Induced subgraph Orbit count |
description |
It is increasingly common to find real-life structures or behaviors represented as graphs in many areas of the computing sciences. Comparing these graphs is a hard task, especially when we are interested in assigning a non-binary similarity score between two large graphs based on some domain-specific context. In bioinformatics, social network analysis and other areas is frequently necessary to compute graph similarities based on the local topological information of each vertex of the given graphs. This is why graphlet degree vectors have become more and more popular in these areas. They provide a simple yet detailed representation of a vertex's topology by counting the number of times such vertex touches a list of small predefined sub-structures called graphlets. In this thesis, we study the state-of-the-art algorithm to compute graphlet degree vectors, the Orbit Counting Algorithm (ORCA). ORCA generates a triangular system of linear equations that can be quickly solved to obtain the graphlet degree vector of a vertex. We make theoretical and practical improvements to this algorithm and measure the difference in speed after these improvements. The theoretical improvement consists of finding automorphisms of graphlets given a fixed vertex that is required to map to itself in such automorphisms. We observe that one piece of the algorithm runs much faster than before with this improvement, especially for larger graphlet orders. This helps the algorithm take less time in generating the linear system that we use to find the desired graphlet degree vector. The practical improvement consists of making a flexible implementation of the algorithm, which can take any graphlet size as input, any number of input graphs, and compute the graphlet degree vector for every vertex in each one of those graphs. |
format |
Text |
author |
Nunez, Wilberto Z |
author_facet |
Nunez, Wilberto Z |
author_sort |
Nunez, Wilberto Z |
title |
Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order |
title_short |
Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order |
title_full |
Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order |
title_fullStr |
Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order |
title_full_unstemmed |
Improvements on ORCA for Fast Computation of Graphlet Degree Vectors of any Graphlet Order |
title_sort |
improvements on orca for fast computation of graphlet degree vectors of any graphlet order |
publisher |
RIT Scholar Works |
publishDate |
2018 |
url |
https://scholarworks.rit.edu/theses/9892 https://scholarworks.rit.edu/context/theses/article/11050/viewcontent/WNunezPichardoThesis8_22_2018.pdf |
genre |
Orca |
genre_facet |
Orca |
op_source |
Theses |
op_relation |
https://scholarworks.rit.edu/theses/9892 https://scholarworks.rit.edu/context/theses/article/11050/viewcontent/WNunezPichardoThesis8_22_2018.pdf |
_version_ |
1770273326668709888 |