Iterative Partitioning with Varying Node Weights

Abstract

The balanced partitioning problem divides the nodes of a [hyper]graph into groups of approximately equal weight (i.e., satisfying balance constraints) while minimizing the number of [hyper]edges that are cut (i.e., adjacent to nodes in different groups). Classic iterative algorithms use the pass paradigm [24] in performing single‐node moves [16, 13] to improve the initial solution. To satisfy particular balance constraints, it is usual to require that intermediate solutions satisfy the constraints. Hence, many possible moves are rejected.Hypergraph partitioning heuristics have been traditionally proposed for and evaluated on hypergraphs with unit node weights only. Nevertheless, many real‐world applications entail varying node weights, e.g., VLSI circuit partitioning where node weight typically represents cell area. Even when multilevel partitioning [3] is performed on unit‐node‐weight hypergraphs, intermediate clustered hypergraphs have varying node weights. Nothing prevents the use of conventional move‐based heuristics when node weights vary, but their performance deteriorates, as shown by our analysis of partitioning results in [1].We describe two effects that cause this deterioration and propose simple modifications of well‐known algorithms to address them. Our baseline implementations achieve dramatic improvements over previously reported results (by factors of up to 25); explicitly addressing the described harmful effects provides further improvement. Overall results are superior to those of the PROP‐REXest algorithm reported in [14], which addresses similar problems.