Existence and construction of a C-shaped module within a floorplan

Abstract

For a given graph, this paper presents a graph-theoretic approach for creating a floorplan with a specific module, i.e., a C-shaped module. Unlike traditional methods that only consider boundary layouts for floorplan generation, this research considers constraints related to constructing the desired modules. The central objective is to explore how graph theoretic properties can ensure the integration of C-shaped modules within floorplans that have rectangular boundaries.

A key innovation lies in introducing the concept of non-triviality for these modules, which becomes crucial for achieving the desired non-trivial C-shaped module (a non-trivial module means that it cannot be transformed into other shaped modules by stretching or shrinking its module walls, i.e. if its module walls are stretched or shrinked, then either the bends of its neighboring modules may increase or the given adjacency may not be preserved).

The proposed solution involves a linear-time algorithm based on the concept of canonical labeling. The algorithm introduces prioritized canonical labeling to generate a non-trivial C-shaped module within the floorplan. It operates on a given plane triangulated graph (PTG) that contains at least one interior $K_4$. The paper outlines the algorithm and establishes the essential conditions for constructing a non-trivial C-shaped module within the floorplan of a given plane triangulated graph (PTG) G. Notably, the algorithm's simplicity and ease of implementation set it apart. In future work, we will focus on generating the existence and construction of other desired shaped modules for the given input graphs.