A Compact Encoding of Rectangular Drawings with Efficient Query Supports

Abstract

A rectangular drawing is a plane drawing in which every face is a rectangle. In this paper we give a simple encoding scheme for rectangular drawings. Given a rectangular drawing Rwith maximum degree 3, our scheme encodes Rwith $\frac{5}{3}m + o(n)$ bits for each n-vertex rectangular drawing R, where mis the number of edges of R, and supports a rich set of queries, including adjacency and degree queries on the faces, in constant time.