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##
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The Min-Max Voronoi Diagram of Polygons and Applications in VLSI Manufacturing
[chapter]

2002
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/3-540-36136-7_45
fatcat:l2gjmnkoyfejxnjferkopkpb7q
*the**min*-*max**Voronoi**diagram**of*a set S*of**polygonal*objects, a generalization*of**Voronoi**diagrams*based on*the*maximum distance between a point*and*a*polygon*. ... As a byproduct we introduce*the**min*-*max*hull which relates to*the*minmax*Voronoi**diagram**in**the*way a convex hull relates to*the*ordinary*Voronoi**diagram*. ... Our motivation for studying*the**min*-*max**Voronoi**diagram*comes from an*application**in**VLSI*yield prediction,*in*particular*the*estimation*of*critical area, a measure reflecting*the*sensitivity*of*a*VLSI*...##
###
L∞ Voronoi Diagrams and Applications to VLSI Layout and Manufacturing
[chapter]

1998
*
Lecture Notes in Computer Science
*

*In*this paper we address

*the*L∞

*Voronoi*

*diagram*

*of*

*polygonal*objects

*and*present

*applications*

*in*

*VLSI*layout

*and*

*manufacturing*. ... Using

*the*L∞

*Voronoi*

*diagram*

*of*

*polygons*we address

*the*problem

*of*calculating

*the*critical area for shorts

*in*a

*VLSI*layout. ...

*In*this paper we present

*applications*

*of*

*Voronoi*

*diagrams*

*in*

*VLSI*layout

*and*

*manufacturing*. ...

##
###
The L_infinity (L_1) Farthest Line-Segment Voronoi Diagram

2012
*
2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
*

well suited for

doi:10.1109/isvd.2012.27
dblp:conf/isvd/DeyP12
fatcat:guxmxeovrrcl3mzymijz47ly6m
*VLSI**applications*. ... We introduce*the*farthest line-segment hull, a closed*polygonal*curve that characterizes*the*regions*of**the*farthest line-segment*Voronoi**diagram*,*and*is related to it similarly to*the*way an ordinary ... ACKNOWLEDGMENT We would like to thank Randolf Schärfig for a GPU implementation*of**the*farthest line-segment*Voronoi**diagram*that provided figures (Fig.1,*and*Fig.13) , Lucia Blondel for a CPU implementation ...##
###
The Hausdorff Voronoi Diagram of Point Clusters in the Plane

2004
*
Algorithmica
*

We study

doi:10.1007/s00453-004-1095-0
fatcat:srwocwmk4bhtdluhaszz4s7fpu
*the*Hausdorff*Voronoi**diagram**of*point clusters*in**the*plane*and*derive a tight combinatorial bound on its structural complexity. ... Motivation for*the*investigation*of*this type*of**Voronoi**diagram*comes from*the*problem*of*computing*the*critical area*of*a*VLSI*Layout, a measure reflecting*the*sensitivity*of**the*design to spot defects ...*In*[3] it was termed*the**Voronoi**diagram**of*point clusters,*in*[1]*the*closest covered set*diagram*,*and**in*[7, 9]*the**min*-*max**Voronoi**diagram*. ...##
###
On the Hausdorff Voronoi Diagram of Point Clusters in the Plane
[chapter]

2003
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-540-45078-8_38
fatcat:ghvta5jlufchnpomxnvfed3opq
*the*Hausdorff*Voronoi**diagram**of*point clusters*in**the*plane*and*derive a tight combinatorial bound on its structural complexity. ... Motivation for*the*investigation*of*this type*of**Voronoi**diagram*comes from*the*problem*of*computing*the*critical area*of*a*VLSI*Layout, a measure reflecting*the*sensitivity*of**the*design to spot defects ...*In*[3] it was termed*the**Voronoi**diagram**of*point clusters,*in*[1]*the*closest covered set*diagram*,*and**in*[7, 9]*the**min*-*max**Voronoi**diagram*. ...##
###
THE HAUSDORFF VORONOI DIAGRAM OF POLYGONAL OBJECTS: A DIVIDE AND CONQUER APPROACH

2004
*
International journal of computational geometry and applications
*

*The*Hausdorff

*Voronoi*

*diagram*finds direct

*application*

*in*

*the*problem

*of*computing

*the*critical area

*of*a

*VLSI*Layout, a measure reflecting

*the*sensitivity

*of*a

*VLSI*design to random

*manufacturing*defects ... Our motivation for studying

*the*Hausdorff

*Voronoi*

*diagram*comes from an

*application*

*in*

*VLSI*

*manufacturing*, namely

*VLSI*yield prediction, as explained

*in*our companion paper. 13

*The*problem statement is ...

*The*

*min*-

*max*

*Voronoi*

*diagram*was formulated to address

*the*critical area computation problem for via-blocks

*in*

*VLSI*designs. ...

##
###
A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of Non-crossing Clusters
[article]

2016
*
arXiv
*
pre-print

*The*

*diagram*finds direct

*applications*

*in*

*VLSI*computer-aided design. ...

*In*

*the*Hausdorff

*Voronoi*

*diagram*

*of*a family

*of*clusters

*of*points

*in*

*the*plane,

*the*distance between a point t

*and*a cluster P is measured as

*the*maximum distance between t

*and*any point

*in*P,

*and*

*the*... Acknowledgements We thank an anonymous reviewer for valuable comments that helped improve

*the*presentation

*of*this paper. ...

##
###
Randomized incremental construction of the Hausdorff Voronoi diagram of non-crossing clusters
[article]

2013
*
arXiv
*
pre-print

*In*

*the*Hausdorff

*Voronoi*

*diagram*

*of*a set

*of*clusters

*of*points

*in*

*the*plane,

*the*distance between a point t

*and*a cluster P is

*the*maximum Euclidean distance between t

*and*a point

*in*P. ... This

*diagram*has direct

*applications*

*in*

*VLSI*design. We consider so-called "non-crossing" clusters. ...

*The*"dual"

*max*-

*min*

*diagram*is

*the*Farthest Color

*Voronoi*

*diagram*[2, 13] . ...

##
###
Computing the Map of Geometric Minimal Cuts
[chapter]

2009
*
Lecture Notes in Computer Science
*

*The*MGMC problem is motivated by

*the*critical area extraction problem

*in*

*VLSI*designs

*and*finds

*applications*

*in*several other fields. ...

*the*complexity

*of*

*the*Hausdorff

*Voronoi*

*diagram*. ... Acknowledgements

*The*authors would like to thank three anonymous referees for their thoughtful comments

*and*suggestions which significantly improve

*the*presentation

*of*

*the*paper. ...

##
###
Computing the Map of Geometric Minimal Cuts

2012
*
Algorithmica
*

*The*MGMC problem is motivated by

*the*critical area extraction problem

*in*

*VLSI*designs

*and*finds

*applications*

*in*several other fields. ...

*the*complexity

*of*

*the*Hausdorff

*Voronoi*

*diagram*. ... Acknowledgements

*The*authors would like to thank three anonymous referees for their thoughtful comments

*and*suggestions which significantly improve

*the*presentation

*of*

*the*paper. ...

##
###
Continuous location of dimensional structures

2004
*
European Journal of Operational Research
*

*of*

*the*nearest-point (farthestpoint)

*Voronoi*

*diagram*. ... Generally, this kind

*of*path appears

*in*problems involving transportation routing design with

*applications*such as oor planning,

*manufacturing*environment design,

*VLSI*layout design, robot moving, etc. ...

##
###
Efficient Max-Norm Distance Computation and Reliable Voxelization
[article]

2003
*
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
*

We present techniques to efficiently compute

doi:10.2312/sgp/sgp03/116-126
fatcat:pk52og4wovcjpgmw2yyncjtopi
*the*distance under*max*-norm between a point*and*a wide class*of*geometric primitives. ...*of*solids*and*generate adaptive distance fields that provides a Hausdorff distance guarantee between*the*boundary*of**the*original primitives*and**the*reconstructed surface. ... We thank Kenny Hoff for his HAVOC software, Joe Warren*and*Scott Schaefer for providing us with dual contouring code,*and**the*reviewers for their feedback*and*suggestions. ...##
###
Optimal Facility Location under Various Distance Functions
[chapter]

1999
*
Lecture Notes in Computer Science
*

*In*

*the*rst we seek a location that maximizes a weighted distance function between

*the*facility

*and*

*the*sites,

*and*

*in*

*the*second we nd a location that minimizes

*the*sum (or sum

*of*

*the*squares)

*of*

*the*distances ... We present ecient algorithms for two problems

*of*facility location.

*In*both problems we want to determine

*the*location

*of*a single facility with respect to n given sites. ... Some

*applications*for this problem are locating a component

*in*a

*VLSI*chip or locating a welding robot

*in*an automobile

*manufacturing*plant. ...

##
###
Rectangular Partitions of a Rectilinear Polygon
[article]

2021
*
arXiv
*
pre-print

We investigate

arXiv:2111.01970v1
fatcat:hqwb4tbicfhvrhr5qp5746srci
*the*problem*of*partitioning a rectilinear*polygon*P with n vertices*and*no holes segments drawn inside P under two optimality criteria. ...*In**the*minimum ink partition,*the*total length*of**the*line segments drawn inside P is minimized. We present an O(n^3)-time algorithm using O(n^2) space that returns a minimum ink partition*of*P. ... There are various*applications**in*chip*manufacturing*[19] , geoinformatics [23] ,*and*pattern recognition [1, 27] . ...##
###
A Survey on Steiner Tree Construction and Global Routing for VLSI Design

2020
*
IEEE Access
*

Steiner tree construction is one

doi:10.1109/access.2020.2986138
fatcat:nqpdbybucjembl4iztn67l4fgi
*of**the*basic models*of**VLSI*physical design, which is usually used*in**the*initial topology creation for noncritical nets*in*physical design. ... Global Routing (GR) is a crucial*and*complex stage*in**the*Very Large-Scale Integration (*VLSI*) design, which minimizes interconnect wirelength*and*delay to optimize*the*overall chip performance. ... [165] proposed a new model based on*the**min*-*max*resource sharing framework. ...
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