Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Optimal orientations of cells in slicing floorplan designs
Information and Control
Interval representations of planar graphs
Journal of Combinatorial Theory Series B
Journal of Algorithms
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
On area-efficient drawings of rectangular duals for VLSI floor-plan
Mathematical Programming: Series A and B
A general approach to dominance in the plane
Journal of Algorithms
On finding the rectangular duals of planar triangular graphs
SIAM Journal on Computing
Coin graphs, polyhedra, and conformal mapping
Proceedings of the 2nd Slovenian conference on Algebraic and topological methods in graph theory
Sliceable Floorplanning by Graph Dualization
SIAM Journal on Discrete Mathematics
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
Rectangular grid drawings of plane graphs
Computational Geometry: Theory and Applications
Classes and recognition of curve contact graphs
Journal of Combinatorial Theory Series B
Graph classes: a survey
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
Box-rectangular drawings of plane graphs
Journal of Algorithms
Representing graphs by disks and balls (a survey of recognition-complexity results)
Discrete Mathematics
A simple linear time algorithm for proper box rectangular drawings of plane graphs
Journal of Algorithms
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Database Management Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Inherent Nonslicibility of Rectangular Duals in VLSI Floorplanning
Proceedings of the Eighth Conference on Foundations of Software Technology and Theoretical Computer Science
Proximity Drawability: a Survey
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Rectangular drawings of planar graphs
Journal of Algorithms
A fast algorithm for area minimization of slicing floorplans
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
GD'10 Proceedings of the 18th international conference on Graph drawing
Contact representations of planar graphs with cubes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Optimal polygonal representation of planar graphs
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Proportional contact representations of planar graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
Linear-time algorithms for hole-free rectilinear proportional contact graph representations
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Computing cartograms with optimal complexity
Proceedings of the twenty-eighth annual symposium on Computational geometry
On representing graphs by touching cuboids
GD'12 Proceedings of the 20th international conference on Graph Drawing
Touching triangle representations for 3-connected planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Proportional contact representations of 4-connected planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
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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 rectangular layouts is a key problem. We study the area-optimization problem and show that it is NP-hard to find a minimum-area rectangular layout of a given contact graph. We present O(n)-time algorithms that construct O(n2)-area rectangular layouts for general contact graphs and O(n log n)-area rectangular layouts for trees. (For trees, this is an O(log n)-approximation algorithm.) We also present an infinite family of graphs (respectively, trees) that require Ω(n2) (respectively, Ω(n log n))area. We derive these results by presenting a new characterization of graphs that admit rectangular layouts, using the related concept of rectangular duals. A corollary to our results relates the class of graphs that admit rectangular layouts to rectangle-of-influence drawings.