SIAM Journal on Computing
Computing the largest empty rectangle
SIAM Journal on Computing
Fast algorithms for computing the largest empty rectangle
SCG '87 Proceedings of the third annual symposium on Computational geometry
Efficient algorithms for identifying all maximal isothetic empty rectangles in VLSI layout design
FST and TC 10 Proceedings of the tenth conference on Foundations of software technology and theoretical computer science
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Widest empty L-shaped corridor
Information Processing Letters
Closed form solution to simultaneous buffer insertion/sizing and wire sizing
Proceedings of the 1997 international symposium on Physical design
Buffer block planning for interconnect-driven floorplanning
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
Algorithms for VLSI Physcial Design Automation
Algorithms for VLSI Physcial Design Automation
Monotone bipartitioning problem in a planar point set with applications to VLSI
ACM Transactions on Design Automation of Electronic Systems (TODAES)
ICCD '91 Proceedings of the 1991 IEEE International Conference on Computer Design on VLSI in Computer & Processors
Channel routing in Manhattan-diagonal model
VLSID '96 Proceedings of the 9th International Conference on VLSI Design: VLSI in Mobile Communication
Routing of L-Shaped Channels, Switchboxes and Staircases in Manhattan-Diagonal Model
VLSID '98 Proceedings of the Eleventh International Conference on VLSI Design: VLSI for Signal Processing
Partitioning VLSI Floorplans by Staircase Channels for Global Routing
VLSID '98 Proceedings of the Eleventh International Conference on VLSI Design: VLSI for Signal Processing
Searching networks with unrestricted edge costs
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Routability-driven repeater block planning for interconnect-centric floorplanning
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On finding a widest empty 1-corner corridor
Information Processing Letters
Hierarchical partitioning of VLSI floorplans by staircases
ACM Transactions on Design Automation of Electronic Systems (TODAES)
On finding widest empty curved corridors
Computational Geometry: Theory and Applications
Nesting of two-dimensional irregular parts: an integrated approach
International Journal of Computer Integrated Manufacturing
On finding a widest empty 1-corner corridor
Information Processing Letters
Recognition of largest empty orthoconvex polygon in a point set
Information Processing Letters
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This paper presents an algorithm for identifying a maximal empty-staircase-polygon (MESP) of largest area, among a set of n points on a rectangular floor. A staircase polygon is an isothetic polygon bounded by two monotonically rising (falling) staircases. A monotonically rising staircase is a sequence of alternatingly horizontal and vertical line segments from the bottom-left corner of the floor to its top-right corner such that for every pair of points α = (xα, yα) and β = (xβ, yβ) on the staircase, xα ≤ xβ implies yα ≤ yβ. A monotonically falling staircase can similarly be defined from the bottom-right corner of the floor to its top-left corner. An empty staircase polygon is a MESP if it is not contained in another larger empty staircase polygon. The problem of recognizing the largest MESP is formulated using permutation graph, and a simple O(n3) time algorithm is proposed. Next, based on certain novel geometric properties of the problem, an improved algorithm is developed that identifies the largest MESP in O(n2) time and space. The algorithm can be easily tailored for identifying the widest MESP in a similar environment. The general problem of locating the largest area/width MESP among a set of isothetic polygonal obstacles, can be solved easily. These geometric optimization problems have several applications to VLSI layout design, robot motion planning, to name a few.