TY - JOUR AU - Sun, Wenbo PY - 2022/06/28 Y2 - 2024/03/28 TI - Sampling and Counting Acyclic Orientations in Chordal Graphs (Student Abstract) JF - Proceedings of the AAAI Conference on Artificial Intelligence JA - AAAI VL - 36 IS - 11 SE - AAAI Student Abstract and Poster Program DO - 10.1609/aaai.v36i11.21667 UR - https://ojs.aaai.org/index.php/AAAI/article/view/21667 SP - 13061-13062 AB - 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 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. ER -