A linear time algorithm for constructing orthogonal floor plans with minimum number of bends

TL;DR

This paper introduces a linear-time algorithm to construct orthogonal floor plans with the minimum number of bends for a given planar triangulated graph, optimizing layout complexity.

Contribution

It presents the first linear-time algorithm for generating OFPs with minimal bends and proves bounds on the minimum number of bends needed.

Findings

Algorithm runs in linear time.

Achieves minimum possible bends in OFPs.

Provides bounds on the number of bends required.

Abstract

Let G = (V, E) be a planar triangulated graph (PTG) having every face triangular. A rectilinear dual or an orthogonal floor plan (OFP) of G is obtained by partitioning a rectangle into \mid V \mid rectilinear regions (modules) where two modules are adjacent if and only if there is an edge between the corresponding vertices in G. In this paper, a linear-time algorithm is presented for constructing an OFP for a given G such that the obtained OFP has B_{min} bends, where a bend in a concave corner in an OFP. Further, it has been proved that at least B_{min} bends are required to construct an OFP for G, where \rho - 2 \leq B_{min} \leq \rho + 1 and \rho is the sum of the number of leaves of the containment tree of G and the number of K_4 (4-vertex complete graph) in G.