Sub-quadratic objectives in quadratic placement

This paper presents a new flexible quadratic and partitioning-based global placement approach which is able to optimize a wide class of objective functions, including linear, sub-quadratic, and quadratic net lengths as well as positive linear combinations of them. Based on iteratively re-weighted quadratic optimization, our algorithm extends the previous linearization techniques. If l is the length of some connection, most placement algorithms try to optimize l¹ or l². We show that optimizing lp with 1 < p < 2 helps to improve even linear connection lengths. With this new objective, our new version of the flow-based partitioning placement tool BonnPlace [25] is able to outperform the state-of-the-art force-directed algorithms SimPL, RQL, ComPLx and closes the gap to MAPLE in terms of (linear) HPWL.