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http://hdl.handle.net/11375/12491
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DC Field | Value | Language |
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dc.contributor.advisor | Deza, Antoine | en_US |
dc.contributor.advisor | Frantisek Franek, Ned Nedialkov | en_US |
dc.contributor.author | Shen, ShengWei | en_US |
dc.date.accessioned | 2014-06-18T16:59:48Z | - |
dc.date.available | 2014-06-18T16:59:48Z | - |
dc.date.created | 2012-09-17 | en_US |
dc.date.issued | 2012-10 | en_US |
dc.identifier.other | opendissertations/7374 | en_US |
dc.identifier.other | 8429 | en_US |
dc.identifier.other | 3326384 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/12491 | - |
dc.description.abstract | <p>Denote by $k_t(G)$ the number of cliques of order $t$ in a graph $G$ having $n$ vertices. Let $k_t(n) = \min\{k_t(G)+k_t(\overline{G}) \}$ where $\overline{G}$ denotes the complement of $G$. Let $c_t(n) = {k_t(n)}/{\tbinom{n}{t}}$ and $c_t$ be the limit of $c_t(n)$ for $n$ going to infinity. A 1962 conjecture of Erd\H{o}s stating that $c_t = 2^{1-\tbinom{t}{2}}$ was disproved by Thomason in 1989 for all $t\geq 4$. Tighter counterexamples have been constructed by Jagger, {\v S}{\v t}ov{\' \i}{\v c}ek and Thomason in 1996, by Thomason for $t\leq 6$ in 1997, and by Franek for $t=6$ in 2002. Further tightenings $t=6,7$ and $8$ was recently obtained by Deza, Franek, and Liu.</p> <p>We investigate the computational framework used by Deza, Franek, and Liu. In particular, we present the benefits and limitations of different parallel computer memory architectures and parallel programming models. We propose a functional decomposition approach which is implemented in C++ with POSIX thread (Pthread) libraries for multi-threading. Computational benchmarking on the parallelized framework and a performance analysis including a comparison with the original computational framework are presented.</p> | en_US |
dc.subject | clique | en_US |
dc.subject | coclique | en_US |
dc.subject | Cayley graph | en_US |
dc.subject | complete graph | en_US |
dc.subject | subgraph | en_US |
dc.subject | parallelization | en_US |
dc.subject | Computer Sciences | en_US |
dc.subject | Discrete Mathematics and Combinatorics | en_US |
dc.subject | Theory and Algorithms | en_US |
dc.subject | Computer Sciences | en_US |
dc.title | On the Parallelization of a Search for Counterexamples to a Conjecture of Erd\H{o}s | en_US |
dc.type | thesis | en_US |
dc.contributor.department | Computer Science | en_US |
dc.description.degree | Master of Science (MSc) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
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fulltext.pdf | 967.08 kB | Adobe PDF | View/Open |
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