eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-12
9:1
9:14
10.4230/LIPIcs.SEA.2020.9
article
Enumerating All Subgraphs Under Given Constraints Using Zero-Suppressed Sentential Decision Diagrams
Nakahata, Yu
1
https://orcid.org/0000-0002-8947-0994
Nishino, Masaaki
2
https://orcid.org/0000-0001-6489-5446
Kawahara, Jun
1
https://orcid.org/0000-0001-7208-044X
Minato, Shin-ichi
1
https://orcid.org/0000-0002-1397-1020
Graduate School of Informatics, Kyoto University, Japan
NTT Communication Science Laboratories, NTT Corporation, Kyoto, Japan
Subgraph enumeration is a fundamental task in computer science. Since the number of subgraphs can be large, some enumeration algorithms exploit compressed representations for efficiency. One such representation is the Zero-suppressed Binary Decision Diagram (ZDD). ZDDs can represent the set of subgraphs compactly and support several poly-time queries, such as counting and random sampling. Researchers have proposed efficient algorithms to construct ZDDs representing the set of subgraphs under several constraints, which yield fruitful results in many applications. Recently, Zero-suppressed Sentential Decision Diagrams (ZSDDs) have been proposed as variants of ZDDs. ZSDDs can be smaller than ZDDs when representing the same set of subgraphs. However, efficient algorithms to construct ZSDDs are known only for specific types of subgraphs: matchings and paths.
We propose a novel framework to construct ZSDDs representing sets of subgraphs under given constraints. Using our framework, we can construct ZSDDs representing several sets of subgraphs such as matchings, paths, cycles, and spanning trees. We show the bound of sizes of constructed ZSDDs by the branch-width of the input graph, which is smaller than that of ZDDs by the path-width. Experiments show that our methods can construct ZSDDs faster than ZDDs and that the constructed ZSDDs are smaller than ZDDs when representing the same set of subgraphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol160-sea2020/LIPIcs.SEA.2020.9/LIPIcs.SEA.2020.9.pdf
Subgraph
Enumeration
Decision Diagram
Zero-suppressed Sentential Decision Diagram (ZSDD)
Top-down construction algorithm