Sampling and Counting Acyclic Orientations in Chordal Graphs (Student Abstract)

Wenbo Sun
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Sampling of chordal graphs and various types of acyclic orientations over chordal graphs plays a central role in several AI applications such as causal structure learning. For a given undirected graph, an acyclic orientation is an assignment of directions to all of its edges which makes the resulting directed graph cycle-free. Sampling is often closely related to the corresponding counting problem. Counting of acyclic orientations of a given chordal graph can be done in polynomial time, but the
more » ... previously known techniques do not seem to lead to a corresponding (efficient) sampler. In this work, we propose a dynamic programming framework which yields a counter and a uniform sampler, both of which run in (essentially) linear time. An interesting feature of our sampler is that it is a stand-alone algorithm that, unlike other DP-based samplers, does not need any preprocessing which determines the corresponding counts.
doi:10.1609/aaai.v36i11.21667 fatcat:6oz5dsg5djcbvl7ckuk22w5j3u