A Theory of L-shaped Floor-plans

TL;DR

This paper extends graph theoretic methods to L-shaped floor-plans, introducing conditions and an efficient algorithm for their construction, broadening the scope beyond rectangular boundary plans.

Contribution

It introduces the concept of non-trivial L-shaped floor-plans and provides necessary and sufficient conditions for their existence, along with an $O(n^2)$ construction algorithm.

Findings

Established conditions for non-trivial L-shaped floor-plans.

Developed an $O(n^2)$ algorithm for constructing such floor-plans.

Extended graph theoretic approaches to non-rectangular boundary plans.

Abstract

Existing graph theoretic approaches are mainly restricted to floor-plans with rectangular boundary. In this paper, we introduce floor-plans with $L$-shaped boundary (boundary with only one concave corner). To ensure the L-shaped boundary, we introduce the concept of non-triviality of a floor-plan. A floor-plan with a rectilinear boundary with at least one concave corner is non-trivial if the number of concave corners can not be reduced, without affecting the modules adjacencies within it. Further, we present necessary and sufficient conditions for the existence of a non-trivial L-shaped floor-plan corresponding to a properly triangulated planar graph (PTPG) $G$. Also, we develop an $O(n^2)$ algorithm for its construction, if it exists.