Related papers: Orientation-Constrained Rectangular Layouts
A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. Rectangular layouts appear in various applications: as rectangular cartograms in cartography, as floorplans in building architecture and…
A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. If…
A rectangular layout $\mathcal{L}$ is a rectangle partitioned into disjoint smaller rectangles so that no four smaller rectangles meet at the same point. Rectangular layouts were originally used as floorplans in VLSI design to represent…
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…
We propose a new generative model for layout generation. We generate layouts in three steps. First, we generate the layout elements as nodes in a layout graph. Second, we compute constraints between layout elements as edges in the layout…
It is common in graphic design humans visually arrange various elements according to their design intent and semantics. For example, a title text almost always appears on top of other elements in a document. In this work, we generate…
We consider the optimal containment of polygonal regions within convex containers with the special property of 'orientedness' - an oriented region enables us to choose a preferred direction on the plane (this direction is not necessarily an…
This paper addresses the challenge of object-centric layout generation under spatial constraints, seen in multiple domains including floorplan design process. The design process typically involves specifying a set of spatial constraints…
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…
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…
We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').
A rectangular floorplan is a partition of a rectangle into smaller rectangles such that no four rectangles meet at a single point. Rectangular floorplans arise naturally in a variety of applications, including VLSI design, architectural…
Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding {\em rectangular layouts} is a key problem. We…
In this paper, cylindric partitions into profiles $c=(1,1)$ and $c=(2,0)$ are considered. The generating functions into unrestricted cylindric partitions and cylindric partitions into distinct parts with these profiles are constructed. The…
A rectilinear polygon is a polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The number of left turns always equals the number of right turns…
We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…
The orientation completion problem for a class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class by orienting the unoriented edges of the partially oriented graph.…
We study the bounded regions in a generic slice of the hyperplane arrangement in $\mathbb{R}^n$ consisting of the hyperplanes defined by $x_i$ and $x_i+x_j$. The bounded regions are in bijection with several classes of combinatorial…