Network partitioning into tree hierarchies

Abstract

ABSTRACT

A network flow approach for hierarchical tree partitioning

“…The experimental results are compared with those of two other recursive partitioning algorithms, GFM and RFM, from [9]. The GFM algorithm uses a bottom-up approach by constructing a hierarchical tree partition from a multiway partition at the bottom level.…”

“…In generalizing the partition structure from two-way and multiway to a tree structure, Vijayan [16] proposed a min-cost tree partitioning which maps a hypergraph H onto the vertices of a tree T, and the cost function to be minimized is the cost to globally route the hyperedges of H on the edges of T. In [9], Kuo et al introduced a hierarchical tree partitioning (HTP) which partitions a netlist into a tree hierarchy subject to a size constraint on partition blocks at each level of the hierarchy. The problem arises when a design is implemented in a hardware hierarchy.…”

“…However, many algorithms that find a reasonably good partition have been developed. As the two-way and multiway partitioning problems, HTP is also NP-hard, even when the tree structure is fixed [9]. To develop heuristic algorithms for it, we can apply some of the approaches used for two-way partitioning and multiway partitioning.…”

“…However, we need to consider the distinct hierarchy and cost function in HTP. In [9], an iterative improvement algorithm based on the Fiduccia-Mattheyses method was proposed to improve an existing initial partition with a fixed tree hierarchy. The initial partition can be generated either randomly or by a constructive algorithm.…”

“…In Section 2, we review the definition of the HTP problem in [9] and formulate it in linear programing by spreading metrics. In Section 3, we will present the network flow based algorithm which consists of two parts: computation of the spreading metric and construction of the hierarchical tree partition.…”