Enumerating Graph Partitions Without Too Small Connected Components Using Zero-suppressed Binary and Ternary Decision Diagrams

TL;DR

This paper introduces an efficient algorithm for enumerating graph partitions with balanced connected components using zero-suppressed decision diagrams, significantly improving speed over previous methods.

Contribution

It presents a novel algorithm combining ZDDs and TDDs for enumerating graph partitions with minimum component weights, enhancing efficiency and scalability.

Findings

Algorithm runs up to tens of times faster than existing methods.

Uses ZDDs and TDDs to handle large search spaces effectively.

Enables enumeration of all desired graph partitions with balanced components.

Abstract

Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However, there are a vast number of graph partitions in a graph, and thus it is difficult to enumerate desired graph partitions efficiently. In this paper, an algorithm to enumerate all the graph partitions such that all the weights of the connected components are at least a specified value is proposed. To deal with a large search space, we use zero-suppressed binary decision diagrams (ZDDs) to represent sets of graph partitions and we design a new algorithm based on frontier-based search, which is a framework to directly construct a ZDD. Our algorithm utilizes not only ZDDs but also ternary decision diagrams (TDDs) and realizes an operation which seems difficult to be designed only by ZDDs. Experimental results show that the proposed algorithm runs up to tens of times faster than an existing state-of-the-art algorithm.