Using helpful sets to improve graph bisections

Multilevel Algorithms for Partitioning Power-Law Graphs

“…A class of partitioning refinement algorithms that are effective in quickly refining the partitioning solution during the uncoarsening phase are those based on variations of the KernighanLin and Fiduccia-Mattheyses algorithms [15,1,5,21,20,10].…”

“…and is similar in nature to the Google dataset and corresponds to a three-level deep crawl out of ten seed CS homepage of major Universities. The PPI dataset is created from Database of Interacting Proteins (DIP) 5 . Each vertex in this graph corresponds to a particular protein and there is an edge between a pair of proteins if these proteins have been experimentally determined to interact with each other.…”

Graph Algorithms for Dynamical Systems

“…Standard methods for local improvement are Kernighan/Lin [KL70] type of algorithms with improvement ideas from Fiduccia/Mattheyses [FM82]. An alternative local improvement heuristic is the Helpful-Set method [DMP95] which is derived from a constructive proof of upper bounds on the bisection width of regular graphs [HM92, MD97, MP01].…”

Application of Fusion-Fission to the Multi-way Graph Partitioning Problem

“…-The PARTY software [PD98]. This software is is based on a multilevel algorithm and a helpful-sets refinement algorithm [DMP95].…”

“…Then, a partition of the coarsenest graph (less than 100 vertices) is built, generally with a graph growing algorithm [KK98a]. After that, the vertices of the partition are successively un-coarsened and the partition refined with a Kernighan-Lin algorithm [KL70,FM82] or a helpful set algorithm [DMP95].…”