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| Content Provider | Society for Industrial and Applied Mathematics (SIAM) |
|---|---|
| Author | Nichterlein, André Hartung, Sepp |
| Copyright Year | 2015 |
| Abstract | In graph realization problems, one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrast, we show NP-completeness for the problem of realizing a given sequence of pairs of nonnegative integers (representing in- and outdegrees) with a directed acyclic graph (DAG), answering an open question of Berger and Müller-Hannemann. Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter maximum degree. Investigating sparse and dense settings, we show that the problem remains NP-hard even if the realizing DAG (precisely, the underlying undirected graph) can be transformed into a clique (a tree) by adding (deleting) a constant fraction of the arcs. In contrast, if at most $k$ arcs have to be inserted, respectively, removed to obtain a clique or a tree in the underlying undirected graph, then the problem becomes fixed-parameter tractable with respect to $k$. |
| Starting Page | 1931 |
| Ending Page | 1960 |
| Page Count | 30 |
| File Format | |
| ISSN | 08954801 |
| DOI | 10.1137/130935756 |
| e-ISSN | 10957146 |
| Journal | SIAM Journal on Discrete Mathematics (SJDMEC) |
| Issue Number | 4 |
| Volume Number | 29 |
| Language | English |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher Date | 2015-10-22 |
| Access Restriction | Subscribed |
| Subject Keyword | Analysis of algorithms and problem complexity combinatorial algorithms graph realization problems parameterized complexity structural parameterization Analysis of algorithms |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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