Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited
Please always quote using this URN: urn:nbn:de:0297-zib-77684
- In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested.
| Author: | Kai-Helge Becker, Benjamin HillerORCiD |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | acyclic orientations; bipolar orientations; enumeration algorithm; multiple sources and sinks |
| MSC-Classification: | 05-XX COMBINATORICS (For finite fields, see 11Txx) |
| 68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) | |
| 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING | |
| CCS-Classification: | J. Computer Applications |
| Date of first Publication: | 2020/03/01 |
| Series (Serial Number): | ZIB-Report (20-05) |
| ISSN: | 1438-0064 |

