Multilevel k-way hypergraph partitioning

Abstract

In this paper, we present a new multilevel k-way hypergraph partitioning algorithm that substantially outperforms the existing state-of-the-art K-PMaLR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on the ISPD98 benchmark suite show that the partitionings produced by our scheme are on the average 15% to 23% better than those produced by the K-PMaLR algorithm, both in terms of the hyperedge cut as well as the (K À 1) metric. Furthermore, our algorithm is signi®cantly faster, requiring 4 to 5 times less time than that required by K-PMaLR.

Gateway finder in large graphs: problem definitions and fast solutions

“…Representative work includes the BANKS system (Aditya et al 2002), link prediction (Liben-Nowell and, content-based image retrieval (He et al 2004), cross-modal correlation discovery (Pan et al 2004), pattern matching (Tong et al 2007), ObjectRank (Balmin et al 2004), RelationalRank (Geerts et al 2004), etc. Other related work in graph mining In recent years, graph mining is a very hot research topic. Representative work includes pattern and law mining (Albert et al 1999;Broder et al 2000), frequent substructure discovery (Jin et al 2005;Xin et al 2005), influence propagation (Kempe et al 2003), fraud and anomaly detection (Neville et al 2005;Noble and Cook 2003), recommendation (Agarwal and Merugu 2007;Cheng et al 2007), community mining and graph partition (Backstrom et al 2006;Chen et al 2009, Gibson et al 1998Girvan and Newman ;Karypis and Kumar 1999;Qian et al 2009), near-clique detection (Pei et al 2005), etc.…”

Developing structural constraints on connectivity for biologically embedded neural networks

“…1b. Special partitioning algorithms, such as HMetis (Karypis and Kumar 2000), have been developed for this kind of graphs. The Rent characteristic derived for hyper-graphs has very different properties compared to the formulation for normal graphs.…”

“…Thus, it can be used to constrain connectivity models not only qualitatively, but also quantitatively. Second, we use hyper-graphs in the description of networks (Karypis and Kumar 2000) in contrast to conventional graphs used in previous studies. While the latter is appropriate for digital circuits, fan-in of which is small and can be accounted for by additional approximations (Stroobandt and Kurdahi 1998), it does not capture the highly branching connectivity of axons and dendrites.…”

Automatic symbolic compositional verification by learning assumptions

“…Many researchers have studied the hypergraph partitioning problem and developed tools, and among them we use hMETIS [24]. hMETIS is a state-of-the-art hypergraph partitioning tool which uses a multilevel k-way partitioning algorithm.…”

“…In addition, the partition provided in the original model may not be the one suitable for compositional reasoning, either in terms of the number of components or the partitioning of functionality among components. Our solution is based on an algorithm for hypergraph partitioning [24,25]. Given a system S with a set of variables X and a desired number n of components, we decompose the set X into n disjoint subsets X 1 , .…”