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Conflict-Free Coloring of Intersection Graphs of Geometric Objects [article]

Chaya Keller, Shakhar Smorodinsky
2017 arXiv   pre-print
In this paper we study conflict-colorings of intersection graphs of geometric objects.  ...  Finally, we present bounds on the number of colors needed for conflict-free colorings of other classes of intersection graphs, including intersection graphs of axis-parallel rectangles and of \rho-fat  ...  Dozens of papers studied conflict-free colorings of graphs and hypergraphs, mostly arising from geometric objects. See the survey [Smo13] and the references therein for more on CF-colorings.  ... 
arXiv:1704.02018v1 fatcat:i7l6nnvd6febjje67gbpt6pwjy

Conflict-Free Coloring of Intersection Graphs [article]

Sándor P. Fekete, Phillip Keldenich
2017 arXiv   pre-print
We demonstrate that the intersection graph of n geometric objects without fatness properties and size restrictions may have conflict-free chromatic number in Ω( n/ n) and in Ω(√( n)) for disks or squares  ...  Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflict-free coloring of geometric intersection graphs.  ...  Most recently, Keller and Smorodinsky [23] consider conflict-free coloring on intersection graphs of geometric objects, in a scenario very similar to ours.  ... 
arXiv:1709.03876v1 fatcat:ssd4liw3sncb5peerltvokuora

Three Colors Suffice: Conflict-Free Coloring of Planar Graphs

Zachary Abel, Victor Alvarez, Erik D. Demaine, Sándor P. Fekete, Aman Gour, Adam Hesterberg, Phillip Keldenich, Christian Scheffer
2017 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms  
a planar bipartite graph has a conflict-free k-coloring.  ...  A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors  ...  Work on this paper was partially supported by the DFG Research Unit "Controlling Concurrent Change", funding number FOR 1800, project FE407/17-2, "Conflict Resolution and Optimization".  ... 
doi:10.1137/1.9781611974782.127 dblp:conf/soda/AbelADFGHKS17 fatcat:swnroxpghrgcbjwzixamj3gb5i

Computational Aspects of Problems on Visibility and Disk Graph Representations [article]

Onur Çağırıcı
2021 arXiv   pre-print
a conflict-free setting, and proper coloring of polygon visibility graphs, for which we have described an algorithm that returns a proper 4-coloring for a simple polygon.  ...  In the field of visibility, we have studied the conflict-free chromatic guarding of polygons, for which we have described a polynomial-time algorithm that uses O(n log^2 n) colors to guard a polygon in  ...  Following the same notation, we write that conflict-free chromatic number χ CF (G) of graph G is the minimum number of colors needed to obtain a conflict-free coloring of G.  ... 
arXiv:2111.00609v1 fatcat:3xl2eklvfffevgpmriawnjynym

Conflict-Free Coloring Made Stronger [chapter]

Elad Horev, Roi Krakovski, Shakhar Smorodinsky
2010 Lecture Notes in Computer Science  
In FOCS 2002, Even et al. showed that any set of n discs in the plane can be Conflict-Free colored with a total of at most O( n) colors.  ...  This framework relates the notion of k-Strong Conflict-Free coloring and the recently studied notion of k-colorful coloring. All of our proofs are constructive.  ...  [17] introduced the notion of Conflict-Free colorings.  ... 
doi:10.1007/978-3-642-13731-0_11 fatcat:h75e2djtg5g5jawhlvl4wb6ny4

On conflict-free coloring of points and simple regions in the plane

Sariel Har-Peled, Shakhar Smorodinsky
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
Acknowledgments The authors would like to thank Pankaj Agarwal, Noga Alon, Boris Aronov, Timothy Chan, Jeff Erickson, Guy Even, János Pach, Rom Pinchasi and Micha Sharir for helpful discussions of the  ...  CF-coloring of Simple Geometric Regions in the Plane Conflict Free Coloring of Rectangles In what follows, we study the conflict free chromatic number of a set of n rectangles in the plane.  ...  We refer to such a coloring as a conflict-free coloring of S.  ... 
doi:10.1145/777792.777810 dblp:conf/compgeom/Har-PeledS03 fatcat:oc6kvsxhc5dcbiadrcdahmg2ym

On conflict-free coloring of points and simple regions in the plane

Sariel Har-Peled, Shakhar Smorodinsky
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
Acknowledgments The authors would like to thank Pankaj Agarwal, Noga Alon, Boris Aronov, Timothy Chan, Jeff Erickson, Guy Even, János Pach, Rom Pinchasi and Micha Sharir for helpful discussions of the  ...  CF-coloring of Simple Geometric Regions in the Plane Conflict Free Coloring of Rectangles In what follows, we study the conflict free chromatic number of a set of n rectangles in the plane.  ...  We refer to such a coloring as a conflict-free coloring of S.  ... 
doi:10.1145/777806.777810 fatcat:vtr4lvscyjdt3bzdzlwmyurana

Safety effectiveness of pavement design treatment at intersections: Left turning vehicles and pedestrians on crosswalks

Hasina Iasmin, Aya Kojima, Hisashi Kubota
2016 IATSS Research  
One of the critical points in pedestrian safety is the occurrence of accidents between left-turning vehicle and pedestrians on crosswalks at signalized intersections.  ...  This study examined the safety effect of three crosswalks designed with different materials such as red-colored material or brick pavement based on a safety performance study.  ...  Acknowledgement This study was conducted under the project "優先配慮行動を促す道 路上の コミュニケーションと交通安全" (Principal Investigator: Ayako Taniguchi, Tsukuba University), supported by The General Insurance Association of  ... 
doi:10.1016/j.iatssr.2016.04.001 fatcat:t4rzgqdpirg4rdauv76tfjukou

FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain Guarding [article]

Akanksha Agrawal, Pradeesha Ashok, Meghana M Reddy, Saket Saurabh, Dolly Yadav
2019 arXiv   pre-print
We also initiate the study of Strong Conflict-free Coloring of graphs.  ...  Given a graph G=(V,E), conflict-free coloring of G refers to coloring a subset of V such that for every vertex v, there is a color that is assigned to exactly one vertex in the closed neighborhood of v  ...  We color v with color 1 . The convex layer is now divided into two halves.  ... 
arXiv:1905.01822v1 fatcat:7kqc2ybmzfgsliti72rtntko2y

Connect-and-Slice: An Hybrid Approach for Reconstructing 3D Objects

Hao Fang, Florent Lafarge
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
Our experiments on a variety of objects and sensors show the versatility of our approach as well as its competitiveness with respect to existing methods.  ...  analysis of the plane connectivity.  ...  Reconstruction of a free-form object at different levels of details. Our algorithm can approximate free-form objects by piecewise planar representations.  ... 
doi:10.1109/cvpr42600.2020.01350 dblp:conf/cvpr/0009L20 fatcat:4bwo5ls2xzdvzmas5b7ywefq6y

Graph Planarity by Replacing Cliques with Paths

Patrizio Angelini, Peter Eades, Seok-Hee Hong, Karsten Klein, Stephen Kobourov, Giuseppe Liotta, Alfredo Navarra, Alessandra Tappini
2020 Algorithms  
Our results contribute to the growing fields of hybrid planarity and of graph drawing beyond planarity.  ...  of h.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a13080194 fatcat:qm3r3iam5nhwnhiiljafaellva

Conflict-Free Coloring of Graphs

Zachary Abel, Victor Alvarez, Erik D. Demaine, Sándor P. Fekete, Aman Gour, Adam Hesterberg, Phillip Keldenich, Christian Scheffer
2018 SIAM Journal on Discrete Mathematics  
[10] consider a certain class of k-degenerate hypergraphs which sometimes arise as intersection graphs of geometric objects, presenting an online algorithm using \scrO (k log n) colors.  ...  This adds to the relevance of conflict-free coloring of planar graphs, which constitute the intersection of general graphs and geometry.  ... 
doi:10.1137/17m1146579 fatcat:uj3b7rzgsbgb3io4j7njd2i6dy

TURNING GAP ACCEPTANCE ON CROSSWALK: IMPACT OF DIFFERENCE ON PAVEMENT

Hasina IASMIN, Aya KOJIMA, Hisashi KUBOTA
2016 Journal of Japan Society of Civil Engineers Ser D3 (Infrastructure Planning and Management)  
Speed of turning vehicle on conflict area during accepting gap is also analyzed to address the severity of interaction occurred by accepting gap.  ...  This study objectives to analyze the likelihood of left and right turning vehicles accepting gaps towards pedestrian considering difference on pavement using logistic regression.  ...  project "Communication Promoting Cooperative Behavior for Other Road Users and Traffic Safety" (Principal Investigator: Ayako Taniguchi, Tsukuba University) supported by The General Insurance Association of  ... 
doi:10.2208/jscejipm.72.i_751 fatcat:5fxpz3a54fg35k5kvyodij25xu

Nice labeling problem for event structures: a counterexample [article]

Victor Chepoi
2011 arXiv   pre-print
structures and median graphs established by Barthélemy and Constantin in 1993.  ...  Our counterexample is based on the Burling's construction from 1965 of 3-dimensional box hypergraphs with clique number 2 and arbitrarily large chromatic numbers and the bijection between domains of event  ...  which we can color the boxes of B in such a way that any pair of intersecting boxes is colored in different colors (i.e., χ(B) is the chromatic number of the intersection graph of the family B).  ... 
arXiv:1107.1207v1 fatcat:ikckspfvwfembdceffudhnkxhm

Collision-Free Motion Algorithms for Sensors Automated Deployment to Enable a Smart Environmental Sensing-Net

Ting-Yu Lin, Kun-Ru Wu, You-Shuo Chen, Yan-Syun Shen
2022 IEEE Transactions on Automation Science and Engineering  
By constructing a conflict graph, we model the collision-free path scheduling as the well-known k-coloring problem, from which we reduce to our k-batching problem (determining the minimum number of required  ...  We observe that the grouping (batching) strategy is similar to the coloring procedure in graph theory.  ...  Our goal is to assign as few collision-free moving groups as possible to all sensors (associated with valid coloring for the conflict graph using as few colors as possible).  ... 
doi:10.1109/tase.2021.3138198 fatcat:kr3gyyrscvd45pztzj7lebg6fu
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