Arbitrarily shaped rectilinear module placement using the transitive closure graph representation

Abstract

Abstract-In this paper, we deal with arbitrarily shaped rectilinear module placement using the transitive closure graph (TCG) representation. The geometric meanings of modules are transparent to TCG as well as its induced operations, which makes TCG an ideal representation for floorplanning/placement with arbitrary rectilinear modules. We first partition a rectilinear module into a set of submodules and then derive necessary and sufficient conditions of feasible TCG for the submodules. Unlike most previous works that process each submodule individually and thus need to perform post processing to fix deformed rectilinear modules, our algorithm treats a set of submodules as a whole and thus not only can guarantee the feasibility of each perturbed solution but also can eliminate the need for the postprocessing on deformed modules, implying better solution quality and running time. Experimental results show that our TCG-based algorithm is capable of handling very complex instances; further, it is very efficient and results in better area utilization than previous work.

A Partition-Based Heuristic Algorithm for the Rectilinear Block Packing Problem

“…Several heuristic methods have been proposed for the rectilinear block packing problem based on different data structures to represent the relationships among the blocks, e.g., BSG (bounded sliceline grid) [8,13], sequence-pairs [5,9,10,17], O-tree [14], B * -tree [16], TCG (transitive closure graph) [11], CBL (corner block list) [12], etc. A special case of the rectilinear block packing problem is the rectangle packing problem.…”