Fixed-Parameter Complexity of Minimum Profile Problems
| dc.creator | Gutin, Gregory | |
| dc.creator | Szeider, Stefan | |
| dc.creator | Yeo, Anders | |
| dc.date | 2006-04-24 | |
| dc.date.accessioned | 2026-07-07T07:09:25Z | |
| dc.date.available | 2026-07-07T07:09:25Z | |
| dc.description | Let $G=(V,E)$ be a graph. An ordering of $G$ is a bijection $α: V\dom \{1,2,..., |V|\}.$ For a vertex $v$ in $G$, its closed neighborhood is $N[v]=\{u\in V: uv\in E\}\cup \{v\}.$ The profile of an ordering $α$ of $G$ is $\prf_α(G)=\sum_{v\in V}(α(v)-\min\{α(u): u\in N[v]\}).$ The profile $\prf(G)$ of $G$ is the minimum of $\prf_α(G)$ over all orderings $α$ of $G$. It is well-known that $\prf(G)$ is the minimum number of edges in an interval graph $H$ that contains $G$ is a subgraph. Since $|V|-1$ is a tight lower bound for the profile of connected graphs $G=(V,E)$, the parametrization above the guaranteed value $|V|-1$ is of particular interest. We show that deciding whether the profile of a connected graph $G=(V,E)$ is at most $|V|-1+k$ is fixed-parameter tractable with respect to the parameter $k$. We achieve this result by reduction to a problem kernel of linear size. | |
| dc.identifier | https://arxiv.org/abs/cs/0604095 | |
| dc.identifier | http://arxiv.org/abs/cs/0604095 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111056 | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | Discrete Mathematics | |
| dc.title | Fixed-Parameter Complexity of Minimum Profile Problems | |
| dc.type | text |