SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Drawing of Two-Dimensional Irregular Meshes
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Drawing Outer-Planar Graphs in O(n log n) Area
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Fractional Lengths and Crossing Numbers
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Straight-Line Drawings of Binary Trees with Linear Area and Arbitrary Aspect Ratio
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Finding small simple cycle separators for 2-connected planar graphs.
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A Dictionary Machine (for VLSI)
IEEE Transactions on Computers
On Embedding Rectangular Grids in Square Grids
IEEE Transactions on Computers
A parallel algorithm for finding a separator in planar graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Optimal vertex ranking of block graphs
Information and Computation
Minimal k-rankings and the rank number of Pn2
Information Processing Letters
The Planar k-Means Problem is NP-Hard
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Minimum Vertex Ranking Spanning Tree Problem on Permutation Graphs
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
A linear-time algorithm to find a separator in a graph excluding a minor
ACM Transactions on Algorithms (TALG)
An On-Line Parallel Algorithm for Node Ranking of Trees
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
IBM Journal of Research and Development
Sliding algorithm for reconfigurable arrays of processors
ICES'07 Proceedings of the 7th international conference on Evolvable systems: from biology to hardware
Greedy algorithms for generalized k-rankings of paths
Information Processing Letters
Graph unique-maximum and conflict-free colorings
Journal of Discrete Algorithms
Max-optimal and sum-optimal labelings of graphs
Information Processing Letters
Small area drawings of outerplanar graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Layout volumes of the hypercube
GD'04 Proceedings of the 12th international conference on Graph Drawing
Small drawings of series-parallel graphs and other subclasses of planar graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
Ordered coloring grids and related graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Graph unique-maximum and conflict-free colorings
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Unique-maximum and conflict-free coloring for hypergraphs and tree graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
The planar k-means problem is NP-hard
Theoretical Computer Science
Ordered coloring of grids and related graphs
Theoretical Computer Science
Circle-Representations of simple 4-regular planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
GD'12 Proceedings of the 20th international conference on Graph Drawing
Finding the edge ranking number through vertex partitions
Discrete Applied Mathematics
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Minimizing the area of a circuit is an important problem in the domain of Very Large Scale Integration. We use a theoretical VLSI model to reduce this problem to one of laying out a graph, where the transistors and wires of the circuit are identified with the vertices and edges of the graph. We give an algorithm that produces VLSI layouts for classes of graphs that have good separator theorems. We show in particular that any planar graph of n vertices has an O(n lg2 n) area layout and that any tree of n vertices can be laid out in linear area. The algorithm maintains a sparse representation for layouts that is based on the well-known UNION-FIND data structure, and as a result, the running time devoted to bookkeeping is nearly linear.