  The modeling flexibility provided by hypergraphs has drawn a lot of interest
from the combinatorial scientific community, leading to novel models and
algorithms, their applications, and development of associated tools.
Hypergraphs are now a standard tool in combinatorial scientific computing. The
modeling flexibility of hypergraphs however, comes at a cost: algorithms on
hypergraphs are inherently more complicated than those on graphs, which
sometimes translate to nontrivial increases in processing times. Neither the
modeling flexibility of hypergraphs, nor the runtime efficiency of graph
algorithms can be overlooked. Therefore, the new research thrust should be how
to cleverly trade-off between the two. This work addresses one method for this
trade-off by solving the hypergraph partitioning problem by finding vertex
separators on graphs. Specifically, we investigate how to solve the hypergraph
partitioning problem by seeking a vertex separator on its net intersection
graph (NIG), where each net of the hypergraph is represented by a vertex, and
two vertices share an edge if their nets have a common vertex. We propose a
vertex-weighting scheme to attain good node-balanced hypergraphs, since NIG
model cannot preserve node balancing information. Vertex-removal and
vertex-splitting techniques are described to optimize cutnet and connectivity
metrics, respectively, under the recursive bipartitioning paradigm. We also
developed an implementation for our GPVS-based HP formulations by adopting and
modifying a state-of-the-art GPVS tool onmetis. Experiments conducted on a
large collection of sparse matrices confirmed the validity of our proposed
techniques.
