Applications of a Novel Sampling Technique to Fully Dynamic Graph Algorithms
| dc.contributor.author | Mountjoy, Benjamin | |
| dc.contributor.supervisor | King, Valerie D. | |
| dc.date.accessioned | 2013-09-11T22:05:15Z | |
| dc.date.available | 2013-09-11T22:05:15Z | |
| dc.date.copyright | 2013 | en_US |
| dc.date.issued | 2013-09-11 | |
| dc.degree.department | Department of Computer Science | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | In this thesis we study the application of a novel sampling technique to building fully-dynamic randomized graph algorithms. We present the following results: \begin{enumerate} \item A randomized algorithm to estimate the size of a cut in an undirected graph $G = (V, E)$ where $V$ is the set of nodes and $E$ is the set of edges and $n = |V|$ and $m = |E|$. Our algorithm processes edge insertions and deletions in $O(\log^2n)$ time. For a cut $(U, V\setminus U)$ of size $K$ for any subset $U$ of $V$, $|U| < |V|$ our algorithm returns an estimate $x$ of the size of the cut satisfying $K/2 \leq x \leq 2K$ with high probability in $O(|U|\log n)$ time. \item A randomized distributed algorithm for maintaining a spanning forest in a fully-dynamic synchronous network. Our algorithm maintains a spanning forest of a graph with $n$ nodes, with worst case message complexity $\tilde{O}(n)$ per edge insertion or deletion where messages are of size $O(\text{polylog}(n))$. For each node $v$ we require memory of size $\tilde{O}(degree(v))$ bits. This improves upon the best previous algorithm with respect to worst case message complexity, given by Awerbuch, Cidon, and Kutten, which has an amortized message complexity of $O(n)$ and worst case message complexity of $O(n^2)$. \end{enumerate} | en_US |
| dc.description.proquestcode | 0984 | en_US |
| dc.description.proquestemail | b_mountjoy9@hotmail.com | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.bibliographicCitation | Bruce M. Kapron, Valerie King, and Ben Mountjoy. Dynamic graph connectivity in polylogarithmic worst case time. In SODA, pages 1131–1142, 2013. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/4926 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | graph algorithm | en_US |
| dc.subject | randomized | en_US |
| dc.subject | distributed graph algorithms | en_US |
| dc.subject | spanning forest | en_US |
| dc.subject | spanning tree | en_US |
| dc.subject | cut size estimation | en_US |
| dc.title | Applications of a Novel Sampling Technique to Fully Dynamic Graph Algorithms | en_US |
| dc.type | Thesis | en_US |