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Enumerating All Subgraphs Under Given Constraints Using Zero-Suppressed Sentential Decision Diagrams

Authors Yu Nakahata , Masaaki Nishino , Jun Kawahara , Shin-ichi Minato

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Author Details

Yu Nakahata
  • Graduate School of Informatics, Kyoto University, Japan
Masaaki Nishino
  • NTT Communication Science Laboratories, NTT Corporation, Kyoto, Japan
Jun Kawahara
  • Graduate School of Informatics, Kyoto University, Japan
Shin-ichi Minato
  • Graduate School of Informatics, Kyoto University, Japan

Funding

This work was supported by JSPS KAKENHI Grant Number JP15H05711, JP18H04091, JP18K04610, and JP19J21000.

Cite As Get BibTex

Yu Nakahata, Masaaki Nishino, Jun Kawahara, and Shin-ichi Minato. Enumerating All Subgraphs Under Given Constraints Using Zero-Suppressed Sentential Decision Diagrams. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SEA.2020.9

Abstract

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Subgraph
  • Enumeration
  • Decision Diagram
  • Zero-suppressed Sentential Decision Diagram (ZSDD)
  • Top-down construction algorithm

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