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Computing minimum feedback arc set to quantify the transitivity in sports teams

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TitleInfo
Title
Computing minimum feedback arc set to quantify the transitivity in sports teams
Name (type = personal)
NamePart (type = family)
Hajeri
NamePart (type = given)
Vishalsingh
NamePart (type = date)
1992-
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Vishalsingh Hajeri
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RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Martin
NamePart (type = given)
Richard P
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Richard P Martin
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Advisory Committee
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chair
Name (type = personal)
NamePart (type = family)
Gajic
NamePart (type = given)
Zoran
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Zoran Gajic
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Advisory Committee
Role
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co-chair
Name (type = personal)
NamePart (type = family)
Patel
NamePart (type = given)
VIshal M
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VIshal M Patel
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Advisory Committee
Role
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co-chair
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NamePart
Rutgers University
Role
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degree grantor
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School of Graduate Studies
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Text
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theses
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DateCreated (qualifier = exact)
2017
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2017-10
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2017
Place
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xx
Language
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eng
Abstract (type = abstract)
This thesis fulfills the need for a system of optimal ranking of sports teams. The current ranking system used for ranking the teams in tournaments like English Premier League (EPL) and Indian Premier League (IPL) only account for wins and losses, while the approach in this thesis better accounts for how teams perform against each other and the relative strength between them, for example, this approach accounts for ’upsets’ where a lower ranked team beats a highly ranked team. A tournament can be represented as a weighted directed graph G, where a directed edge E from team A to team B represents that Team A beat Team B and the edge weight constitutes the Goal Difference (GD) or the points differential between the two teams for that particular match. A feedback arc set (FAS) of G is a subset of its edges which contains at least one edge of every cycle in G. These set of edges which when removed from G, leaves us with a Directed Acyclic graph (DAG). The aim of this project is to solve ’Minimum Feedback Arc Set problem’ (MFAS) which in other words is removing minimum number of least weighted edges from G such that the remainder of the graph G’ results in a DAG. We solved the minimum feedback arc set problem by framing it as an optimization problem and utilized Gurobi Optimization Library to get the results. A linear Ordering of the resulting DAG gives the ranking of teams in the tournament. Sub-part of this project is to calculate Coefficient of Transitivity (CoT) of a Tournament. The transitivity of a sports tournament would manifest itself as when a Team A, dominated Team B with a large point differential, and Team B dominated Team C, then Team A should also dominate Team C. However, if Team C beats Team A then we call it as an ’upset’ and such upsets gives rise to cycles in the tournament graph G and thus decreases the transitive nature of the tournament. An important finding of this project is that the balance among sports tournaments like Soccer, Football and Cricket can be characterized by calculating the CoT for a particular season.
Subject (authority = RUETD)
Topic
Electrical and Computer Engineering
Subject (authority = ETD-LCSH)
Topic
Mathematical optimization
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD
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ETD_8305
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (ix, 38 p. : ill.)
Note (type = degree)
M.S.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Vishalsingh Hajeri
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TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T35M68T6
Genre (authority = ExL-Esploro)
ETD graduate
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Rights

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The author owns the copyright to this work.
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Name
FamilyName
Hajeri
GivenName
Vishalsingh
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2017-08-23 16:27:39
AssociatedEntity
Name
VISHALSINGH HAJERI
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Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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