Joseph W. H. Liu
Abstract
A heuristic graph partitioning scheme is presented to determine effective node separators for undirected graphs. An initial separator is first obtained from the minimum degree ordering, an algorithm designed originally to produce fill-reducing orderings for sparse matrices. The separator is then improved by an iterative strategy based on some known results from bipartite graph matching. This gives an overall practical scheme in partitioning graphs. Experimental results are provided to demonstrate the effectiveness of this heuristic algorithm on graphs arising from sparse matrix applications.
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Index Terms
- A graph partitioning algorithm by node separators
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Reviews
Douglas M. Campbell
The divide-and-conquer paradigm partitions an undirected graph into smaller components through the removal of a (small) set of nodes. Practicality dictates balancing the time taken to create the partition with the time saved by the creation of smaller subproblems. One important application of partitioning is VLSI design. By modeling circuits as graphs, the layout problem can be reduced to mapping graphs into layouts in an area-efficient manner. A small set of edges is removed from the graph to reduce the graph to smaller pieces. After laying out the smaller pieces, the designer modifies the layout to account for the small set of missing edges. The construction continues recursively. Fast algorithms to construct such separator sets are known for trees and planar graphs. This paper provides an effective algorithm to partition an arbitrary undirected graph. The author surveys the history and known results of such separators. He shows the connection between graph separators and sparse matrix partitioning. The paper contains a detailed illustration of the method. It concludes with experimental results for graphs arising from sparse matrix applications. This paper is a pleasant balance of theory and practice.
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