A general framework for vertex orderings with applications to circuit clustering

This work presents a vertex ordering construction that encompasses most reasonable graph traversals and uses dynamic programming to optimality split the vertex ordering into a multiway clustering.

Abstract

Vertex orderings have been successfully applied to problems in netlist clustering and for system partitioning and layout. We present a vertex ordering construction that encompasses most reasonable graph traversals. Two parameters-an attraction function and a window-provide the means for achieving various graph traversals and addressing particular clustering requirements. We then use dynamic programming to optimality split the vertex ordering into a multiway clustering. Our approach outperforms several clustering methods in the literature in terms of three distinct clustering objectives. The ordering construction, by itself, also outperforms existing graph ordering constructions for this application. Tuning our approach to "meta-objectives", particularly clustering for two-phase Fiduccia-Mattheyses bipartitioning, remains an open area of research.