# A New Efficient Topological Structure for Floorplanning in 3D VLSI Physical Design

### Ajoy Kumar Khan, Rahul Vatsa and Sudipta Roy

Department of Information Technology

Assam University

Silchar, India

Department of CSE

North Eastern Regional Institute of Science and Technology

Nirjuli, India

Abstract—Floor planning is a key problem in VLSI physical design. The floor planning problem can be formulated as that a given set of 3D rectangular blocks while minimizing suitable cost functions. Here, we are concentrating on the minimization of the total volume of 3D die. In this paper, first we propose a new topological structure using weighted directed graph of a floor planning problem in 3D VLSI physical design. But here the main question is this structure is effective or not. For this, we give the idea of a new algorithm to minimize the volume of 3D die in floor planning problem using this new representation technique. It is interesting to see that our proposed structure is also capable to calculate the total volume and position of the dead spaces if dead spaces exist. Next, we give the experimental result of our new algorithm and then conclude the paper.

Keywords : floorplanning, 3-D rectangular block, weighted directed graph, topological structure, volume.

1 Introduction

One of the most important steps of VLSI physical design is floor planning. The goal of floor planning is to arrange some non-overlapping blocks so that a certain objective function is minimized. The objective function may be total area for 2D, total volume in 3D of a floor plan, total wire length etc.

Two popular approaches to floor planning, simulated annealing and analytical formulation are typically used to solve the floor planning problem in 2D. The simulated annealing process is based on the topological relation between the modules but the analytical formulation process is based on mathematical programming to compose of an objective function and a set of constraints. In addition modern VLSI floor planning also needs to handle some important issues such as soft modules and fixed-outline constraints. In soft module the area of module is decided during floor planning. So, we need a particular algorithm for floor planning.