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University of St Andrews

1.
Menezes, Nina E.
* Random* generation and chief length of finite groups.

Degree: PhD, 2013, University of St Andrews

URL: http://hdl.handle.net/10023/3578

Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, and we specify this list and provide exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150. In Part II we consider a related notion. Given a probability ε, we wish to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G), the minimal number of generators needed to generate G. We obtain bounds on the chief length of permutation groups in terms of the degree n, and bounds on the chief length of completely reducible matrix groups in terms of the dimension and field size. Combining these with existing bounds on d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely reducible matrix groups.

Subjects/Keywords: 512; Finite group theory; Random generation; Chief length; Probabilistic group theory; Almost simple groups; Permutation groups; Matrix groups; Computational group theory; Group theory

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Menezes, N. E. (2013). Random generation and chief length of finite groups. (Doctoral Dissertation). University of St Andrews. Retrieved from http://hdl.handle.net/10023/3578

Chicago Manual of Style (16^{th} Edition):

Menezes, Nina E. “Random generation and chief length of finite groups.” 2013. Doctoral Dissertation, University of St Andrews. Accessed July 11, 2020. http://hdl.handle.net/10023/3578.

MLA Handbook (7^{th} Edition):

Menezes, Nina E. “Random generation and chief length of finite groups.” 2013. Web. 11 Jul 2020.

Vancouver:

Menezes NE. Random generation and chief length of finite groups. [Internet] [Doctoral dissertation]. University of St Andrews; 2013. [cited 2020 Jul 11]. Available from: http://hdl.handle.net/10023/3578.

Council of Science Editors:

Menezes NE. Random generation and chief length of finite groups. [Doctoral Dissertation]. University of St Andrews; 2013. Available from: http://hdl.handle.net/10023/3578

2. Sharma, Abhishek. High throughput path selection for unstructured data center networks.

Degree: MS, 0112, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/45451

The increase in demand and popularity of cloud and big data applications has driven the need for higher throughput data center network design. Recent work to provide topologies with much denser interconnects pose a difficult challenge for routing of traffic within a data center. Even with proposals like MPTCP that improve upon TCP, there is a still a gap between theoretical throughput and empirical throughput.
Our goal is to study routing in data centers at both flow and packet-level to determine the cause of inefficiency and study methods of path selection that may help bridge the gap between optimal throughput and packet level throughput. The difference in throughput can be attributed to inefficiency due to path selection and inefficiency due to protocol overhead; we quantify the contribution of each. Focusing on path selection, our experiments show that k-disjoint paths provide much better throughput in most topologies than the previously used k-shortest paths. We also show that one can positively impact network throughput by varying the number of paths according to network density.
*Advisors/Committee Members: Godfrey, Philip B. (advisor).*

Subjects/Keywords: Data Center; Multipath Transmission Control Protocol (MPTCP); Jellyfish; Shortest Paths; Disjoint Paths; Throughput; Random Regular Graph (RRG); Random Permutation Matrix; Switches; Servers; Ports; Network Density

…computed once the *random* regular graph and traffic *matrix*
has been constructed.
We tested and… …*random* *permutation* traffic i.e. each source server randomly selects a
destination server to… …from *random* *permutation* traffic.
3.4
Throughput computation
In our experiments, we have… …are all conducted on the Jellyfish topology. The topology
is essentially a *random* regular… …commodity network flow problem on the traffic *matrix*. We use
the CPLEX linear programming solver…

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Sharma, A. (2013). High throughput path selection for unstructured data center networks. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45451

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Sharma, Abhishek. “High throughput path selection for unstructured data center networks.” 2013. Thesis, University of Illinois – Urbana-Champaign. Accessed July 11, 2020. http://hdl.handle.net/2142/45451.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Sharma, Abhishek. “High throughput path selection for unstructured data center networks.” 2013. Web. 11 Jul 2020.

Vancouver:

Sharma A. High throughput path selection for unstructured data center networks. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jul 11]. Available from: http://hdl.handle.net/2142/45451.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sharma A. High throughput path selection for unstructured data center networks. [Thesis]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45451

Not specified: Masters Thesis or Doctoral Dissertation