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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.

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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)
CCS-Classification:J. Computer Applications
Date of first Publication:2020/03/01
Series (Serial Number):ZIB-Report (20-05)
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