Preserving large cuts in fully dynamic graphs
| dc.contributor.author | Wasim, Omer | |
| dc.contributor.supervisor | King, Valerie D. | |
| dc.date.accessioned | 2020-05-22T02:47:37Z | |
| dc.date.available | 2020-05-22T02:47:37Z | |
| dc.date.copyright | 2020 | en_US |
| dc.date.issued | 2020-05-21 | |
| dc.degree.department | Department of Computer Science | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | This thesis initiates the study of the MAX-CUT problem in fully dynamic graphs. Given a graph $G=(V,E)$, we present the first fully dynamic algorithms to maintain a $\frac{1}{2}$-approximate cut in sublinear update time under edge insertions and deletions to $G$. Our results include the following deterministic algorithms: i) an $O(\Delta)$ \textit{worst-case} update time algorithm, where $\Delta$ denotes the maximum degree of $G$ and ii) an $O(m^{1/2})$ amortized update time algorithm where $m$ denotes the maximum number of edges in $G$ during any sequence of updates. \\ \indent We also give the following randomized algorithms when edge updates come from an oblivious adversary: i) a $\tilde{O}(n^{2/3})$ update time algorithm\footnote{Throughout this thesis, $\tilde{O}$ hides a $O(\text{polylog}(n))$ factor.} to maintain a $\frac{1}{2}$-approximate cut, and ii) a $\min\{\tilde{O}(n^{2/3}), \tilde{O}(\frac{n^{{3/2}+2c_0}}{m^{1/2}})\}$ worst case update time algorithm which maintains a $(\frac{1}{2}-o(1))$-approximate cut for any constant $c_0>0$ with high probability. The latter algorithm is obtained by designing a fully dynamic algorithm to maintain a sparse subgraph with sublinear (in $n$) maximum degree which approximates all large cuts in $G$ with high probability. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/11764 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | algorithms | en_US |
| dc.subject | data structures | en_US |
| dc.subject | graph algorithms | en_US |
| dc.subject | fully dynamic | en_US |
| dc.subject | sublinear update | en_US |
| dc.title | Preserving large cuts in fully dynamic graphs | en_US |
| dc.type | Thesis | en_US |