14 research outputs found
Compact Floor-Planning via Orderly Spanning Trees
Floor-planning is a fundamental step in VLSI chip design. Based upon the
concept of orderly spanning trees, we present a simple O(n)-time algorithm to
construct a floor-plan for any n-node plane triangulation. In comparison with
previous floor-planning algorithms in the literature, our solution is not only
simpler in the algorithm itself, but also produces floor-plans which require
fewer module types. An equally important aspect of our new algorithm lies in
its ability to fit the floor-plan area in a rectangle of size (n-1)x(2n+1)/3.
Lower bounds on the worst-case area for floor-planning any plane triangulation
are also provided in the paper.Comment: 13 pages, 5 figures, An early version of this work was presented at
9th International Symposium on Graph Drawing (GD 2001), Vienna, Austria,
September 2001. Accepted to Journal of Algorithms, 200
Orientation-Constrained Rectangular Layouts
We construct partitions of rectangles into smaller rectangles from an input
consisting of a planar dual graph of the layout together with restrictions on
the orientations of edges and junctions of the layout. Such an
orientation-constrained layout, if it exists, may be constructed in polynomial
time, and all orientation-constrained layouts may be listed in polynomial time
per layout.Comment: To appear at Algorithms and Data Structures Symposium, Banff, Canada,
August 2009. 12 pages, 5 figure
The Flip Diameter of Rectangulations and Convex Subdivisions
We study the configuration space of rectangulations and convex subdivisions
of points in the plane. It is shown that a sequence of
elementary flip and rotate operations can transform any rectangulation to any
other rectangulation on the same set of points. This bound is the best
possible for some point sets, while operations are sufficient and
necessary for others. Some of our bounds generalize to convex subdivisions of
points in the plane.Comment: 17 pages, 12 figures, an extended abstract has been presented at
LATIN 201
Towards Characterizing Graphs with a Sliceable Rectangular Dual
\u3cp\u3eLet G be a plane triangulated graph. A rectangular dual of G is a partition of a rectangle R into a set R of interior-disjoint rectangles, one for each vertex, such that two regions are adjacent if and only if the corresponding vertices are connected by an edge. A rectangular dual is sliceable if it can be recursively subdivided along horizontal or vertical lines. A graph is rectangular if it has a rectangular dual and sliceable if it has a sliceable rectangular dual. There is a clear characterization of rectangular graphs. However, a full characterization of sliceable graphs is still lacking. The currently best result (Yeap and Sarrafzadeh, 1995) proves that all rectangular graphs without a separating 4-cycle are slice- able. In this paper we introduce a recursively defined class of graphs and prove that these graphs are precisely the nonsliceable graphs with exactly one separating 4-cycle.\u3c/p\u3
Embedding the dual complex of hyper-rectangular partitions
A rectangular partition is the partition of an (axis-aligned) rectangle into
interior-disjoint rectangles. We ask whether a rectangular partition permits a
"nice" drawing of its dual, that is, a straight-line embedding of it such that
each dual vertex is placed into the rectangle that it represents. We show that
deciding whether such a drawing exists is NP-complete. Moreover, we consider
the drawing where a vertex is placed in the center of the represented rectangle
and consider sufficient conditions for this drawing to be nice. This question
is studied both in the plane and for the higher-dimensional generalization of
rectangular partitions