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
Applications of generalized matrix searching to geometric algorithms
Discrete Applied Mathematics - Computational combinatiorics
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Geometric discrepancy theory and uniform distribution
Handbook of discrete and computational geometry
Enclosing k points in the smallest axis parallel rectangle
Information Processing Letters
Hot Spots and Zones in a Chip: A Geometrician's View
VLSID '05 Proceedings of the 18th International Conference on VLSI Design held jointly with 4th International Conference on Embedded Systems Design
Cell-level placement for improving substrate thermal distribution
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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In this era of giga-scale integration, thermal analysis has become one of the hot topics in VLSI chip design. Active thermal sources may be abstracted as a set of weighted points on a 2D chip-floor. The conventional notion of discrepancy that deals with the congestion properties of a set of scattered points may not be able to capture properly all real-life instances in this context. In this paper, we have introduced a new concept, called the density of a region to study some of the properties of the distribution of these weighted points. We prove several counter-intuitive results concerning the properties of the regions that have maximum or minimum density. We then outline algorithms for recognizing these regions. We also compare the attributes of density with the existing concept of discrepancy.