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Minimum Constraint Removal Problem for Line Segments is NP-hard [article]

Bahram Sadeghi Bigham
<span title="2021-07-07">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, using a reduction from Subset Sum problem, in three steps, we show that the problem is NP-hard for both weighted and unweighted line segments.  ...  However, it has a simple linear solution when constraints are lines and the problem is open for other cases yet.  ...  Minimum Constraint Removal Problem The minimum constraint removal or briefness M CR was first introduced by Houser in 2013 [Hauser, 2013] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2107.03140v1">arXiv:2107.03140v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/urgg2siehvadtoolqcmnkuvolm">fatcat:urgg2siehvadtoolqcmnkuvolm</a> </span>
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Hardness and Approximation of Minimum Convex Partition [article]

Nicolas Grelier
<span title="2021-12-21">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The approximation results are obtained by relating the problem to the Covering Points with Non-Crossing Segments problem. We show that this problem is NP-hard, and present an FPT algorithm.  ...  Those hardness and approximation results also holds for the Minimum Convex Tiling problem, defined similarly but allowing the use of Steiner points.  ...  We also show NP-hardness of a similar problem, which we call Minimum Convex Tiling problem (MCT).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.07697v3">arXiv:1911.07697v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3k5aajdkmbeqzcwg3i6ttv3b7m">fatcat:3k5aajdkmbeqzcwg3i6ttv3b7m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201009191004/https://arxiv.org/pdf/1911.07697v2.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.07697v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Computing Partitions of Rectilinear Polygons with Minimum Stabbing Number [chapter]

Stephane Durocher, Saeed Mehrabi
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show that finding a conforming rectangular partition of minimum stabbing number is NP-hard for rectilinear polygons with holes.  ...  The stabbing number of a partition of a rectilinear polygon P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment contained in P .  ...  They also show that, for a given point set, the problems of finding a spanning tree or a triangulation with minimum stabbing number are NP-hard.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-32241-9_20">doi:10.1007/978-3-642-32241-9_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jce52qviqrfslmkwffwfntmun4">fatcat:jce52qviqrfslmkwffwfntmun4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170428004339/http://saeedmehrabi.com/papers/cocoon2012.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/30/f630898c5a28146f88aad30e02992ab538099ec7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-32241-9_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the approximability of covering points by lines and related problems

Adrian Dumitrescu, Minghui Jiang
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/is2k7576zbherpepqy3y7zkzuy" style="color: black;">Computational geometry</a> </i> &nbsp;
As a geometric variant of SET COVER, COVERING POINTS BY LINES is still NP-hard.  ...  Given a set P of n points in the plane, COVERING POINTS BY LINES is the problem of finding a minimum-cardinality set L of lines such that every point p ∈ P is incident to some line ℓ ∈ L.  ...  [31] , for suggesting the extension to lines-in our Theorem 1-of the result from [11] (Theorem 1, p. 1041) for line segments, and for pertinent advice on polynomial representation of points on circular  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.comgeo.2015.06.006">doi:10.1016/j.comgeo.2015.06.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rh4ghiurgzb4beas226gdbwj7q">fatcat:rh4ghiurgzb4beas226gdbwj7q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150827175247/http://www.cs.uwm.edu/faculty/ad/line-cover.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/e0/a4e083964d0bfede29397b30a683bb90d22f1955.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.comgeo.2015.06.006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Complexity of minimum corridor guarding problems

Ning Xu
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5xfy4fcdxvcvdiybp6iqbffqc4" style="color: black;">Information Processing Letters</a> </i> &nbsp;
In this paper, the complexity of minimum corridor guarding problems is discussed.  ...  These problems are proved to be NP-complete.  ...  Acknowledgment This work is supported by a NSF grant(No. 1017539). The author thanks Peter Brass for his valuable comments and helpful suggestions related to the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2012.06.003">doi:10.1016/j.ipl.2012.06.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/az7garf6zrccrcn6gkfowtr33e">fatcat:az7garf6zrccrcn6gkfowtr33e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190428042330/https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=1029&amp;context=cc_etds_theses" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3a/dd/3add360b353e867026e76591d7bd22d6f8419604.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2012.06.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Beyond connecting the dots: A polynomial-time algorithm for segmentation and boundary estimation with imprecise user input

Thomas Windheuser, Thomas Schoenemann, Daniel Cremers
<span title="">2009</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/753trptklbb4nj6jquqadzwwdu" style="color: black;">2009 IEEE 12th International Conference on Computer Vision</a> </i> &nbsp;
In this sense, the user input can be seen as a soft constraint. We prove that the resulting optimization problem is NP-hard.  ...  We propose a polynomial-time algorithm for segmentation and (open) boundary estimation which takes into account a series of user-specified attraction points.  ...  This problem is known as the Euclidean Traveling Salesman Problem and was shown to be NP-hard [6] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iccv.2009.5459281">doi:10.1109/iccv.2009.5459281</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iccv/WindheuserSC09.html">dblp:conf/iccv/WindheuserSC09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jug6d4uav5fddk2lhentmqvqwm">fatcat:jug6d4uav5fddk2lhentmqvqwm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100525073719/http://www.robots.ox.ac.uk:80/~vgg/rg/papers/beyonddots.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/c7/94c75a666989a2039a4e667878eb486292030d41.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iccv.2009.5459281"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Optimal positioning of surveillance UGVs

U. Nilsson, P. Ogren, J. Thunberg
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dmucnarmarh2fj6syg5jyqs7ny" style="color: black;">2008 IEEE/RSJ International Conference on Intelligent Robots and Systems</a> </i> &nbsp;
., in response to an alarm, is needed. In this paper we focus on two problems. The first is how to create a line-of-sight perimeter around a given set of buildings with a minimal number of UGVs.  ...  The second problem is how to find UGV positions such that a given set of walls are covered by the cameras while taking constraints in terms of zoom, range, resolution and field of view into account.  ...  This problem is known to be NP-hard, [12] , and furthermore even finding a set of guards whose cardinality is at most 1 + times the optimum is also NP-hard, [13] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2008.4650851">doi:10.1109/iros.2008.4650851</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iros/NilssonOT08.html">dblp:conf/iros/NilssonOT08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g5t5ogkgjzbnvdu5t2vos473c4">fatcat:g5t5ogkgjzbnvdu5t2vos473c4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180305023107/http://www.csc.kth.se:80/~petter/Publications/ugvPositioning_iros_final.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1c/4a/1c4a7cd162ea675b3e98f6b140a148136a8b9782.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2008.4650851"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

On the Complexity of Clustering with Relaxed Size Constraints [chapter]

Massimiliano Goldwurm, Jianyi Lin, Francesco Saccà
<span title="">2016</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Moreover, we prove that in the Euclidean plane, i.e. assuming dimension 2 and 2-norm, the problem is NP-hard even with size constraints set reduced to M = {2, 3}.  ...  We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the 1-norm an  ...  Acknowledgments We thank an anonymous referee for his/her useful comments on other problems related to clustering with relaxed size constraints.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-41168-2_3">doi:10.1007/978-3-319-41168-2_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g4uouolskzaqtds2ccl4tefwiy">fatcat:g4uouolskzaqtds2ccl4tefwiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923025407/https://air.unimi.it/retrieve/handle/2434/426429/663193/aaim-8.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/85/f5/85f5682b1e60cf6384ba6cc542439a2999d897f4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-41168-2_3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Minimum Hidden Guarding of Histogram Polygons [article]

Hamid Hoorfar, Alireza Bagheri
<span title="2017-08-19">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is known that the problem is NP-hard for simple polygon with general visibility and it is true for simple orthogonal polygon.  ...  In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility.  ...  The art gallery problem is also NP-hard for orthogonal polygons [21] and it even remains NP-hard for monotone polygons [21] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.05815v1">arXiv:1708.05815v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6kfnjzvfk5cmbjab6fprdwtbhm">fatcat:6kfnjzvfk5cmbjab6fprdwtbhm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200827060306/https://arxiv.org/pdf/1708.05815v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e4/69/e469b4fab9f8617e177cfe0e14d45976013f7290.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.05815v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Restricted vertex multicut on permutation graphs

Charis Papadopoulos
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
The problem is known to be NP-complete for trees and polynomial-time solvable for interval graphs. In this paper we give a polynomial-time algorithm for the problem on permutation graphs.  ...  Given an undirected graph and pairs of terminals the Restricted Vertex Multicut problem asks for a minimum set of nonterminal vertices whose removal disconnects each pair of terminals.  ...  Thus for many interesting and even constraint graph classes (e.g., cographs, split graphs, and co-bipartite graphs) the Unrestricted Vertex Multicut problem is already NP-hard.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2012.03.021">doi:10.1016/j.dam.2012.03.021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q4n7w65nhfgj7o6y4rvcsuecse">fatcat:q4n7w65nhfgj7o6y4rvcsuecse</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120714012144/http://www.cs.uoi.gr/~charis/files/Multicut-permutation.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/04/d4/04d4d78bbd79ac7bfe736af72a895d52cd0bfb09.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2012.03.021"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Improved approximation bounds for the minimum constraint removal problem

Sayan Bandyapadhyay, Neeraj Kumar, Subhash Suri, Kasturi Varadarajan
<span title="">2020</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/is2k7576zbherpepqy3y7zkzuy" style="color: black;">Computational geometry</a> </i> &nbsp;
., Improved approximation bounds for the minimum constraint removal problem, Comput.  ...  We also present some inapproximability results for the geometric constraint removal problem.  ...  The problem is known to be NP-complete even when the obstacles have very simple geometry such as rectangles or line segments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.comgeo.2020.101650">doi:10.1016/j.comgeo.2020.101650</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6wh32jm6w5g5fn4nbyn3qn7mca">fatcat:6wh32jm6w5g5fn4nbyn3qn7mca</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200403020637/https://pdf.sciencedirectassets.com/271512/AIP/1-s2.0-S0925772120300444/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEEkaCXVzLWVhc3QtMSJHMEUCIHKwptaVgDN91Hz9EJTddCwjCOs%2F56ay09BQ9o6WvQHsAiEAyXX%2BzLl2L0QwCnLFgcRmeC7%2Fpf3516cUr9hGy%2Bp35kQqtAMIUhACGgwwNTkwMDM1NDY4NjUiDKdssuHxSuxKyJxeWiqRA9jrVcnZHr8G9xax7TbuW7WF1AclwNR2GUu%2B00GjoJ1Y%2BWiTNfHNp06DDVckQSNHtOT8ZvX2VDrcA1Lg6gy3OvgPqd1ksmCrf2OsH0f%2BI6YzjRT6ERtYcgwE5AbI3hhWX5utFetCLovG9ME7DOzP%2BGT9cZjL5LaYUgnxFKTvCvBwOOE3P0aYcxUwhYzExJ3A31bxLWEqQp2TEBmeyTiBZKz%2Bs3h4QipCIApgnxydXXPILl2DlfzcLITjmXweobVc7NT%2B8x6ys%2Fnd4uIXjngf1dAtl8bzPjj%2BOpNAN2P6tCqgi5aNKLbkpletdvBTmsmMopMeJv%2BMRftAmiWzp20VwqWUsh5c26rBkSh6KGWnVT4zaLeOW5vYCLFigJKPHGfkLfZhmdRUkxgJ%2BqISaZL6Di2h6F7NKQBpjIcmB3BLLLpOXFYt%2BqB%2BGRExVO%2FsGGabV5Tj%2FvZn5LsmcxEA8TCtRhkN4uFS%2FOU7FXNNKkTZ%2Fr331p5eVRTllGtHk0ZHSqd2G98GFY7WcfpE9JceKDU4XNy6MNKJmvQFOusB0KZP%2FRwNWZCTqYBYYl8e1Vn4yoHb6Ko%2Fz%2Bo1Uqi1%2FK5ecdjgACYcElPZ5z9qaLD%2FoL8vnr9uwpcuG4ty7goJVxxaI4ZCNmdjB2IOywVRSC6qyUoPDhbBaTMggDComsGwMYeWOtD%2FDP6daJa2mn8h1a%2BTDQATcbcO1pWG5Y0reYSJyIu6ltOk2GiEHzEOLQvV%2BujscEyc98x0IkmVzSEV01UUwEYwI5rMKXvZfaSvM0bcCSY%2BRUD3wLycBGKCL%2BbiuRHhUDedhmcWbNJTUvgHLaFR2mSjnUuX9zE0q%2BFlQzOg37sOlQIlp7kxbQ%3D%3D&amp;X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20200403T020632Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=300&amp;X-Amz-Credential=ASIAQ3PHCVTY4JVJXD56%2F20200403%2Fus-east-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=5ab8fef29924a0b5146a8b9cd1e9202cebc353a941d5be2b3e9065ad9c9817bc&amp;hash=00bdae9f8b1e9e1c66a8d8a5bec9ba6b2c2684131f2d8aa43aec5115aad7125e&amp;host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&amp;pii=S0925772120300444&amp;tid=spdf-f01b8e63-0bbb-4949-95be-30d9be26d489&amp;sid=50c2bad487532647da4a78e361d90c5792a5gxrqa&amp;type=client" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.comgeo.2020.101650"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Non-crossing paths with geographic constraints [article]

Rodrigo I. Silveira, Bettina Speckmann, Kevin Verbeek
<span title="2019-01-25">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that when paths must be drawn as straight line segments, it is NP-complete to determine if a crossing-free solution exists, even if all vertical segments have unit length.  ...  In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn without crossings?  ...  In particular, they show that our problem for vertical segment regions and straight line segment paths is NP-hard, a fact that was also proven earlier in the Master's thesis of one of the authors of the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.05486v3">arXiv:1708.05486v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oflzdcw5lvbvve3y4axeyy725q">fatcat:oflzdcw5lvbvve3y4axeyy725q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200911084853/https://arxiv.org/pdf/1708.05486v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/40/bf4074f29b1d52e6a905614c6a44f4d93ed6e560.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.05486v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Constraint-driven clustering

Rong Ge, Martin Ester, Wen Jin, Ian Davidson
<span title="">2007</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fqqihtxlu5bvfaqxjyvqcob35a" style="color: black;">Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD &#39;07</a> </i> &nbsp;
We prove the NP-hardness of the CDC problem with different constraints.  ...  Two general types of constraints are considered, i.e. minimum significance constraints and minimum variance constraints, as well as combinations of these two types.  ...  We have proved the NP-hardness of the proposed CDC problem with difference constraints.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1281192.1281229">doi:10.1145/1281192.1281229</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/kdd/GeEJD07.html">dblp:conf/kdd/GeEJD07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j2antwvidzasjcdz7lmnzhwjdm">fatcat:j2antwvidzasjcdz7lmnzhwjdm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812032237/http://web.cs.ucdavis.edu/~davidson/constrained-clustering/CAREER/rong.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1a/ef/1aef8839a1233c80d1f6b86f591802abee0e4f3b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1281192.1281229"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

SFCDecomp: Multicriteria Optimized Tool Path Planning in 3D Printing using Space-Filling Curve Based Domain Decomposition [article]

Prashant Gupta, Yiran Guo, Narasimha Boddeti, Bala Krishnamoorthy
<span title="2021-09-04">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We first show that the minimum turn cost 3d printing problem is NP-hard, even when the region is a simple polygon.  ...  We explore efficient optimization of toolpaths based on multiple criteria for large instances of 3d printing problems.  ...  [5] showed that the minimum length lawn mowing problem for polygonal regions with or without holes is NP-hard, and the minimum length milling problem for polygon regions with holes is also NP-hard.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.01769v1">arXiv:2109.01769v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dyuw5xrgkrheffaoqipj4u2yzu">fatcat:dyuw5xrgkrheffaoqipj4u2yzu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210909183542/https://arxiv.org/pdf/2109.01769v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b2/4c/b24c90e21085c69a31aa6c7bf508c87e6cbed5c9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.01769v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Energy-constrained bi-objective data muling in underwater wireless sensor networks

Ke Li, Chien-Chung Shen, Guaning Chen
<span title="">2010</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kwegstofqzcrrcyrpviq5g7dtq" style="color: black;">The 7th IEEE International Conference on Mobile Ad-hoc and Sensor Systems (IEEE MASS 2010)</a> </i> &nbsp;
We design two heuristic algorithms to solve one special case and one generalized case of this NP-hard problem, respectively.  ...  For underwater wireless sensor networks (UWSNs), data muling is an effective approach to data gathering, where sensor data are collected when a mobile data mule travels within the wireless communication  ...  NP-hard.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mass.2010.5664026">doi:10.1109/mass.2010.5664026</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/mass/LiSC10.html">dblp:conf/mass/LiSC10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h2kxzrnm2rdhte6fhcuocvuo24">fatcat:h2kxzrnm2rdhte6fhcuocvuo24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808222844/https://www.eecis.udel.edu/~cshen/861/papers/udmp.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/6a/bf6aca91dc3ec53fa9940f8b534f70f31597c8eb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mass.2010.5664026"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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