A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On the stab number of rectangle intersection graphs
[article]

2018
*
arXiv
*
pre-print

A lower bound

arXiv:1804.06571v1
fatcat:m23w5dsxxram7ibms7bipswy2i
*on**the**stab**number**of**rectangle**intersection**graphs*in terms*of*its pathwidth and clique*number*is shown. ... We introduce*the*notion*of**stab**number*and exact*stab**number**of**rectangle**intersection**graphs*, otherwise known as*graphs**of*boxicity at most 2. ... In Section 4, we show a lower bound*on**the**stab**number**of**rectangle**intersection**graphs*in terms*of**the*clique*number*and*the*pathwidth, and then study upper bounds*on**the**stab**number**of**rectangle**intersection*...##
###
Development of Algorithm for Identification of Area for Maximum Coverage and Interference

2017
*
International Journal of Computer Applications
*

For a point set P in convex position, derive a lower bound

doi:10.5120/ijca2017915323
fatcat:xl7t2a6z7nfava2hou2mwls5qu
*on**the*size*of**the**stabbing*set axis-parallel*rectangles*induced by each pair*of*points a,b∈P as*the*diagonal*of**the**rectangles*. ... For a point set P, where no two points have*the*same x or y coordinates, derive an upper bound*on**the*size*of**the**stabbing*set*of*axis-parallel*rectangles*induced by each pair*of*points a,b ∈ P as*the*... Proximity*graph*[1] is a*graph*where*the*edges between*the*vertices*of**the**graphs*depend*on**the*neighbourlines*of**the*vertices. ...##
###
Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

2013
*
Discrete & Computational Geometry
*

Several classical constructions illustrate

doi:10.1007/s00454-013-9534-9
fatcat:sccdix27orhd5p2ucvcdfchhvq
*the*fact that*the*chromatic*number**of*a*graph*can be arbitrarily large compared to its clique*number*. ... However, until very recently, no such construction was known for*intersection**graphs**of*geometric objects in*the*plane. ... Open Access This article is distributed under*the*terms*of**the*Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided*the*original author(s) ...##
###
Greedy is good: An experimental study on minimum clique cover and maximum independent set problems for randomly generated rectangles
[article]

2012
*
arXiv
*
pre-print

., R_n}

arXiv:1212.0640v1
fatcat:eccdsw3ryvhn7f2ugn3obw4mcq
*of*n randomly positioned axis parallel*rectangles*in 2D,*the*problem*of*computing*the*minimum clique cover (MCC) and maximum independent set (MIS) for*the**intersection**graph*G( R)*of**the*members ... Finally we will provide refined greedy algorithms based*on*a concept*of*simplicial*rectangle*. ... Thus,*the*minimum clique cover*of**the**graph*G(R) is same as*the*minimum*number**of*points required to*stab*all*the**rectangles*inR. ...##
###
On a special class of boxicity 2 graphs
[article]

2016
*
arXiv
*
pre-print

A 2SIG is an axes-parallel

arXiv:1603.09561v1
fatcat:phzx2lo6dbardfzll7nvwny2vy
*rectangle**intersection**graph*where*the**rectangles*have unit height (that is, length*of**the*side parallel to Y-axis) and*intersects*either*of**the*two fixed lines, parallel to ... We define and study a class*of**graphs*, called 2-*stab*interval*graphs*(2SIG), with boxicity 2 which properly contains*the*class*of*interval*graphs*. ... Now consider axes-parallel*rectangles*with unit height (length*of**the*side parallel to Y -axis) that*intersects**one**of**the**stab*lines. ...##
###
Fixed-parameter algorithms for Cochromatic Number and Disjoint Rectangle Stabbing via iterative localization

2013
*
Information and Computation
*

This NP-complete problem is equivalent to deciding whether

doi:10.1016/j.ic.2013.08.007
fatcat:toybexwo6ranvlcvskka7aidju
*the*cochromatic*number**of*a given permutation*graph**on*n vertices is at most k. ... Our algorithm solves in fact a more general problem: within*the*mentioned running time, it decides whether*the*cochromatic*number**of*a given perfect*graph**on*n vertices is at most k. ... Recall that a*rectangle*is*stabbed*by a line if their*intersection*is nonempty. ...##
###
Fixed-Parameter Algorithms for Cochromatic Number and Disjoint Rectangle Stabbing
[chapter]

2010
*
Lecture Notes in Computer Science
*

In fact, we give a more general result: within

doi:10.1007/978-3-642-13731-0_32
fatcat:mstvuiwhhjgkfmnfegcx35lmmi
*the*mentioned running time,*one*can decide whether*the*cochromatic*number**of*a given perfect*graph**on*n vertices is at most k. ... This NP-complete problem is equivalent to deciding whether*the*cochromatic*number*, partitioning into*the*minimum*number**of*cliques or independent sets,*of*a given permutation*graph**on*n vertices is at ... Section 3 gives an overview*of**the*method we use to solve Cochromatic*Number**on*perfect*graphs*and Disjoint*Rectangle**Stabbing*. ...##
###
Parameterized Complexity of Stabbing Rectangles and Squares in the Plane
[chapter]

2009
*
Lecture Notes in Computer Science
*

k, select at most k

doi:10.1007/978-3-642-00202-1_26
fatcat:7mguax2wwjgljjsoykn7ilokpe
*of**the*lines such that every*rectangle*is*intersected*by at least*one**of**the*selected lines. ... For*the*special case*of**Rectangle**Stabbing*where all*rectangles*are squares*of**the*same size we can also show W[1]-hardness, while*the*parameterized complexity*of**the*special case where*the*input consists ... We thank Dániel Marx, who pointed us to*the*approach for proving that*Rectangle**Stabbing*is in W [1] . ...##
###
A note on maximum independent sets in rectangle intersection graphs

2004
*
Information Processing Letters
*

Finding

doi:10.1016/j.ipl.2003.09.019
fatcat:oeg6ftox3rb2nlmqfuk7wqmyti
*the*maximum independent set in*the**intersection**graph**of*n axis-parallel*rectangles*is NP-hard. We re-examine two known approximation results for this problem. ... similar algorithm running in only O(n log n + n∆ k−1 ) time, where ∆ ≤ n denotes*the*maximum*number**of**rectangles*a point can be in. ... , or equivalently, find a maximum independent set in*the**intersection**graph**of**the**rectangles*. ...##
###
Independent Sets of Dynamic Rectangles: Algorithms and Experiments
[article]

2020
*
arXiv
*
pre-print

We study

arXiv:2002.07611v1
fatcat:v6zkwzunsrd7hfvqy6kozrsboa
*the*maximal independent set (MIS) and maximum independent set (MAX-IS) problems*on*dynamic sets*of*O(n) axis-parallel*rectangles*, which can be modeled as dynamic*rectangle**intersection**graphs*. ... We conclude with an algorithm that maintains a 2-approximate MAX-IS for dynamic sets*of*uniform height and arbitrary width*rectangles*with O(ωlog n) update time, where ω is*the*largest*number**of*maximal ... ., that every*rectangle*in R is*stabbed*by exactly*one*line in H. For a set*of**rectangles*R, we denote*the*subset*stabbed*by a line h j as R(h j ) ⊆ R. ...##
###
Extension complexity of stable set polytopes of bipartite graphs
[article]

2017
*
arXiv
*
pre-print

*The*extension complexity xc(P)

*of*a polytope P is

*the*minimum

*number*

*of*facets

*of*a polytope that affinely projects to P. ... Let G be a bipartite

*graph*with n vertices, m edges, and no isolated vertices. Let

*STAB*(G) be

*the*convex hull

*of*

*the*stable sets

*of*G. It is easy to see that n ≤xc (

*STAB*(G)) ≤ n+m. ... We thank Monique Laurent and Ronald de Wolf for bringing

*the*topic

*of*this paper to our attention. ...

##
###
All-Pairs Shortest Paths in Geometric Intersection Graphs

2018
*
Journal of Computational Geometry
*

Specifically we reduce

doi:10.20382/jocg.v10i1a2
dblp:journals/jocg/ChanS19
fatcat:7n4nsty24fcrdnjrpko43piuke
*the*problem to*the*design*of*static data structures for offline*intersection*detection. ... Thus, we obtain an $\OO{n \log n}$-time SSSP algorithm in unweighted*intersection**graphs**of*$n$ axis-aligned line segments. ... To derive our result for*intersection**graphs**of*axis-aligned boxes, we describe in Section 5 a new O n √ log n -time algorithm for oine*rectangle**stabbing*in two dimensions: preprocess n axis-aligned*rectangles*...##
###
Covering and Packing of Rectilinear Subdivision
[article]

2018
*
arXiv
*
pre-print

(P1)

arXiv:1809.07214v1
fatcat:cpf7ifgbnbavhc7t67qjyorov4
*Stabbing*-Subdivision:*Stab*all bounded faces by selecting a minimum*number**of*points in*the*plane. ... We study a class*of*geometric covering and packing problems for bounded regions*on**the*plane. ... In [6] , Gaur et al. studied*the**rectangle**stabbing*problem. Here [6] given a set*of**rectangles*,*the*objective is to*stab*all*rectangles*with a minimum*number**of*axis-parallel lines. ...##
###
Visibility Representations of Boxes in 2.5 Dimensions
[article]

2016
*
arXiv
*
pre-print

Finally, we prove that deciding whether a given

arXiv:1608.08899v1
fatcat:nklafeuyvbcfjoxhqcsklznn74
*graph*G admits a 2.5D-GBR with a given footprint is NP-complete.*The*footprint*of*a 2.5D-BR Γ is*the*set*of*bottom faces*of**the*boxes in Γ. ... We initiate*the*study*of*2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having*the*bottom face in*the*plane z=0 and edges are unobstructed lines*of*sight parallel to ... We now prove that if h and v both*stab*ten boxes, there must be*one*box that is*stabbed*by both h and v , which implies that*the**number**of*boxes in Γ is at most 19. ...##
###
Extended formulations from communication protocols in output-efficient time
[article]

2019
*
arXiv
*
pre-print

Although constructive, those tools are not output-efficient, since

arXiv:1811.08529v2
fatcat:yva327pz5ndalmxqh5m4huxodq
*the*time needed to produce*the*extended formulation also depends*on**the**number**of*rows*of**the*slack matrix (hence,*on**the*exact description ... ~Yannakakis' extended formulation for*the*stable set polytope*of*perfect*graphs*, for which, to*the*best*of*our knowledge, an efficient construction was previously not known. ... We thank Mihalis Yannakakis for inspiring discussions and Samuel Fiorini for useful comments*on*[1] , where many*of**the*results here presented appeared. ...
« Previous

*Showing results 1 — 15 out of 854 results*