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Parameterized Hardness of Art Gallery Problems

Édouard Bonnet, Tillmann Miltzow
2020 ACM Transactions on Algorithms  
The Vertex Guard Art Gallery problem asks for 4 such a set S subset of the vertices of P. A point in the set S is referred to as a guard.  ...  The Point Guard Art Gallery problem asks for a minimum set 3 S such that every point in P is visible from a point in S.  ...  In order to achieve these results, we slightly extend some known hardness results of geometric 97 set cover/hitting set problems and combine them with problem-specific insights of the art gallery 98 problem  ... 
doi:10.1145/3398684 fatcat:25gzjq2u2bbkhi3pte4wqj5awy

The Parameterized Hardness of the Art Gallery Problem [article]

Édouard Bonnet, Tillmann Miltzow
2017 arXiv   pre-print
The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P. A point in the set S is referred to as a guard.  ...  The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S.  ...  Despite the recent successes of parameterized complexity, only very few results on the art gallery problem are known.  ... 
arXiv:1603.08116v2 fatcat:ou2xlkjpmvbljgaj6jfyt6rmw4

Parameterized Hardness of Art Gallery Problems *

Édouard Bonnet, Tillmann Miltzow
unpublished
The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P. A point in the set S is referred to as a guard.  ...  The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S.  ...  NP-hardness and APX-hardness have been shown for many variants of the art gallery problem and other related problems [11, 23, 4, 26] .  ... 
fatcat:i46avqw6bfdh3mxisot3pr5vjm

The Parameterized Complexity of Guarding Almost Convex Polygons

Akanksha Agrawal, Kristine V. K. Knudsen, Daniel Lokshtanov, Saket Saurabh, Meirav Zehavi, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry  
The Art Gallery problem is a fundamental visibility problem in Computational Geometry.  ...  Apart from being a variant of Art Gallery, this case can also be viewed as the classic Dominating Set problem in the visibility graph of a polygon.  ...  Giannopoulos's Parameterization and Our Contribution In light of the W [1] -hardness result by Bonnet and Miltzow [5] , Giannopoulos [10] proposed to parameterize the Art Gallery problem by the number  ... 
doi:10.4230/lipics.socg.2020.3 dblp:conf/compgeom/AgrawalKL0Z20 fatcat:ojkrkrplhfgt5gaigushtkt77q

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
This problem is NP-hard even for k=1 and therefore under standard complexity theoretic assumptions, FPT algorithms do not exist when parameterised by the solution size.  ...  We consider the k-Conflict-free Coloring problem parameterised by the treewidth of the graph and show that this problem is fixed parameter tractable.  ...  We further study the parameterized complexity of the chromatic art gallery problem and the conflict free art gallery problem.  ... 
arXiv:1905.01822v1 fatcat:7kqc2ybmzfgsliti72rtntko2y

The Parameterized Complexity of Guarding Almost Convex Polygons [article]

Akanksha Agrawal, Kristine V.K. Knudsen, Daniel Lokshtanov, Saket Saurabh, Meirav Zehavi
2020 arXiv   pre-print
Art Gallery is a fundamental visibility problem in Computational Geometry.  ...  Recently, three new important discoveries were made: the above mentioned variants of Art Gallery are all W[1]-hard with respect to k [Bonnet and Miltzow, ESA'16], the classic variant has an O(log k)-approximation  ...  The classic variant of Art Gallery is the Point-Point Art Gallery problem.  ... 
arXiv:2003.07793v1 fatcat:agnxduu3jfaa3gpv2u3ksjsxji

Topological Art in Simple Galleries [article]

Daniel Bertschinger, Nicolas El Maalouly, Tillmann Miltzow, Patrick Schnider, Simon Weber
2021 arXiv   pre-print
Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P.  ...  Furthermore, for various concrete topological spaces T, we describe instances I of the art gallery problem such that V(I) is homeomorphic to T.  ...  Parameterized hardness of art gallery problems. ACM Transactions on Algorithms, 16(4), 2020. [12] Dorit Borrmann, Pedro J. de Rezende, Cid C. de Souza, Sándor P.  ... 
arXiv:2108.04007v1 fatcat:qifivyhmgrbzrn4fridq2iw2aq

Stabbing Polygonal Chains with Rays is Hard to Approximate

Steven Chaplick, Elad Cohen, Gila Morgenstern
2013 Canadian Conference on Computational Geometry  
Additionally, it is hard to approximate within a factor of 7 6 even when the curves are line segments with bounded slopes.  ...  We show that this problem is hard to approximate within a logarithmic factor even when the curves are convex polygonal x-monotone chains.  ...  Introduction Motivated by art-gallery problems such as terrainguarding and minimum-link watchman route, Katz, Mitchell and Nir [7] studied a family of geometric stabbing/hitting problems involving orthogonal  ... 
dblp:conf/cccg/ChaplickCM13 fatcat:cbb3ax5jzngkpntcroo2pwguye

Exact Algorithms for Terrain Guarding

Pradeesha Ashok, Fedor V. Fomin, Sudeshna Kolay, Saket Saurabh, Meirav Zehavi
2018 ACM Transactions on Algorithms  
Given a 1.5-dimensional terrain T , also known as an x-monotone polygonal chain, the Terrain Guarding problem seeks a set of points of minimum size on T that guards all of the points on T .  ...  In spite of the remarkable developments in approximation algorithms for Terrain Guarding, next to nothing is known about its parameterized complexity.  ...  The reduction given in [4] also implies that Art Gallery is W[1]-hard parameterized by k. Thus it is highly unlikely that Art Gallery is fixed-parameter tractable (FPT).  ... 
doi:10.1145/3186897 fatcat:bvp4eyqlv5fxnfwker2dnk7kie

Know You at One Glance: A Compact Vector Representation for Low-Shot Learning

Yu Cheng, Jian Zhao, Zhecan Wang, Yan Xu, Karlekar Jayashree, Shengmei Shen, Jiashi Feng
2017 2017 IEEE International Conference on Computer Vision Workshops (ICCVW)  
proposed method over state-of-the-arts.  ...  Low-shot face recognition is a very challenging yet important problem in computer vision. The feature representation of the gallery face sample is one key component in this problem.  ...  The work of Jiashi Feng was partially supported by National University of Singapore startup grant R-263-000-C08-133 and Ministry of Education of Singapore AcRF Tier One grant R-263-000-C21-112.  ... 
doi:10.1109/iccvw.2017.227 dblp:conf/iccvw/ChengZWXKSF17 fatcat:vzzdc32oajfp7davfg2qd6umeu

Orthogonal Terrain Guarding is NP-complete

Édouard Bonnet, Panos Giannopoulos, Marc Herbstritt
2018 International Symposium on Computational Geometry  
Terrain Guarding can be seen as a special case of the famous art gallery problem where one has to place at most k guards on a terrain made of n vertices in order to fully see it.  ...  They ask if Orthogonal Terrain Guarding is in P or NP-hard.  ...  The principal remaining open questions concern the parameterized complexity of terrain guarding. (1) Is Terrain Guarding FPT parameterized by the number of guards?  ... 
doi:10.4230/lipics.socg.2018.11 dblp:conf/compgeom/BonnetG18 fatcat:eslflf4nivechlpn3odmpdse34

A Virtual Reconstruction of a Virtual Exhibit [chapter]

Thomas F. Banchoff, Davide P. Cervone
2002 Mathematics and Visualization  
Inspired by the virtual art gallery "Surfaces Beyond the Third Dimension", itself based on a physical exhibit originally staged by the Providence Art Club in 1996, this updated version includes new images  ...  We describe here the process, and some of the difficulties, of putting together such a project.  ...  Figure 1 . 1 From a view of the Providence Art Club's Dodge House gallery (left), the user can click on any wall and get a close-up view of that area of the gallery (right).  ... 
doi:10.1007/978-3-642-56240-2_2 fatcat:52ufr7ha5ve2jievwcemnfvlue

Generalizable Person Re-Identification by Domain-Invariant Mapping Network

Jifei Song, Yongxin Yang, Yi-Zhe Song, Tao Xiang, Timothy M. Hospedales
2019 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
To make the model domain-invariant, we follow a meta-learning pipeline and sample a subset of source domain training tasks during each training episode.  ...  When such a model is trained on a set of source domains (ReID datasets collected from different camera networks), it can be directly applied to any new unseen dataset for effective ReID without any model  ...  is the encoding subnet parameterized by φ. f θ (·) is the classifier parameterized by θ where θ ∈ R D×C .  ... 
doi:10.1109/cvpr.2019.00081 dblp:conf/cvpr/SongYSXH19 fatcat:ndec575rjzhibnziwf5mhx536e

Orthogonal Terrain Guarding is NP-complete [article]

Édouard Bonnet, Panos Giannopoulos
2018 arXiv   pre-print
Terrain Guarding can be seen as a special case of the famous art gallery problem where one has to place at most $k$ guards on a terrain made of $n$ vertices in order to fully see it.  ...  They ask if Orthogonal Terrain Guarding is in P or NP-hard.  ...  Introduction Terrain Guarding is a natural restriction of the well-known art gallery problem.  ... 
arXiv:1710.00386v2 fatcat:db5sahext5hj3iei5vuvdz72u4

Open Problems in Evolutionary Music and Art [chapter]

Jon McCormack
2005 Lecture Notes in Computer Science  
Five 'open problems' are defined and explained as broad principle areas of investigation for evolutionary music and art.  ...  Applying evolutionary methods to the generation of music and art is a relatively new field of enquiry.  ...  What Is Art? In answer to the question 'what is art?' Frieder Nake proposed that anything exhibited in art galleries is art [19] .  ... 
doi:10.1007/978-3-540-32003-6_43 fatcat:atvvdzuccfastpiv4rhlfh7qgi
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