Relevant bibliographies by topics / Geometric Covering and Packing

Academic literature on the topic 'Geometric Covering and Packing'

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Published: 6 September 2023

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Journal articles on the topic "Geometric Covering and Packing"

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Chan, Timothy M., and Elyot Grant. "Exact algorithms and APX-hardness results for geometric packing and covering problems." Computational Geometry 47, no. 2 (February 2014): 112–24. http://dx.doi.org/10.1016/j.comgeo.2012.04.001.

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Ashok, Pradeesha, Aniket Basu Roy, and Sathish Govindarajan. "Local search strikes again: PTAS for variants of geometric covering and packing." Journal of Combinatorial Optimization 39, no. 2 (June 21, 2019): 618–35. http://dx.doi.org/10.1007/s10878-019-00432-y.

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Klevanskiy, Nikolay N., Sergey I. Tkachev, Ludmila A. Voloshchuk, Rouslan B. Nourgaziev, and Vladimir S. Mavzovin. "Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions." Applied Sciences 11, no. 11 (May 31, 2021): 5128. http://dx.doi.org/10.3390/app11115128.

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A new approach to investigate the two-dimensional, regular packing of arbitrary geometric objects (GOs), using cognitive visualization, is presented. GOs correspond to congruent non-convex polygons with their associated coordinate system. The origins of these coordinate systems are accepted by object poles. The approach considered is based on cognitive processes that are forms of heuristic judgments. According to the first heuristic judgment, regular packing of congruent GOs on the plane have a honeycomb structure, that is, each GO contacts six neighboring GO, the poles of which are vertices of the pole hexagon in the honeycomb construction of packing. Based on the visualization of the honeycomb constructions a second heuristic judgment is obtained, according to which inside the hexagon of the poles, there are fragments of three GOs. The consequence is a third heuristic judgment on the plane covering density with regular packings of congruent GOs. With the help of cognitive visualization, it is established that inside the hexagon of poles there are fragments of exactly three objects. The fourth heuristic judgment is related to the proposal of a triple lattice packing for regular packing of congruent GOs.
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Tyrin, Grigory, and Vladimir Frolovsky. "Research and application of the crow search algorithm for geometric covering optimization problems." Proceedings of the Russian higher school Academy of sciences, no. 1 (July 8, 2021): 54–61. http://dx.doi.org/10.17212/1727-2769-2021-1-54-61.

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The problem of geometric covering is a special case of the optimal design problem and belongs to the class of cutting and packing problems. The challenge is to position some geometric objects on the surface to be coated so that the entire surface is covered. The complexity of the problems under consideration is due to their belonging to the class of NP-hard problems, which excludes the possibility of solving them by exact methods and requires the development of approximate optimization methods and algorithms. This article discusses the problem of geometric covering of an area with circles from a given set of radii. To solve the problem of geometric covering, a hexagonal grid coverage method with optimization by a metaheuristic algorithm is used. The crow search algorithm is such an algorithm, which is a relatively new metaheuristic algorithm based on the intelligent behavior of crows in a flock. The crow search algorithm includes two control parameters: the awareness probability and the flight length. To study the solution method and check the efficiency, a problem was modeled on the basis of a real design of automatic irrigation systems, and the results of experiments with different values of control parameters were presented.
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Fejes Tóth, G., P. Gritzmann, and J. M. Wills. "Finite sphere packing and sphere covering." Discrete & Computational Geometry 4, no. 1 (January 1989): 19–40. http://dx.doi.org/10.1007/bf02187713.

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Swanepoel, Konrad J. "Simultaneous Packing and Covering in Sequence Spaces." Discrete & Computational Geometry 42, no. 2 (May 7, 2009): 335–40. http://dx.doi.org/10.1007/s00454-009-9189-8.

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MATTILA, PERTTI, and R. DANIEL MAULDIN. "Measure and dimension functions: measurability and densities." Mathematical Proceedings of the Cambridge Philosophical Society 121, no. 1 (January 1997): 81–100. http://dx.doi.org/10.1017/s0305004196001089.

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During the past several years, new types of geometric measure and dimension have been introduced; the packing measure and dimension, see [Su], [Tr] and [TT1]. These notions are playing an increasingly prevalent role in various aspects of dynamics and measure theory. Packing measure is a sort of dual of Hausdorff measure in that it is defined in terms of packings rather than coverings. However, in contrast to Hausdorff measure, the usual definition of packing measure requires two limiting procedures, first the construction of a premeasure and then a second standard limiting process to obtain the measure. This makes packing measure somewhat delicate to deal with. The question arises as to whether there is some simpler method for defining packing measure and dimension. In this paper, we find a basic limitation on this possibility. We do this by determining the descriptive set-theoretic complexity of the packing functions. Whereas the Hausdorff dimension function on the space of compact sets is Borel measurable, the packing dimension function is not. On the other hand, we show that the packing dimension functions are measurable with respect to the σ-algebra generated by the analytic sets. Thus, the usual sorts of measurability properties used in connection with Hausdorff measure, for example measures of sections and projections, remain true for packing measure.
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Groemer, H. "Some basic properties of packing and covering constants." Discrete & Computational Geometry 1, no. 2 (June 1986): 183–93. http://dx.doi.org/10.1007/bf02187693.

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Böröczky, Károly. "Finite packing and covering by congruent convex domains." Discrete & Computational Geometry 30, no. 2 (July 10, 2003): 185–93. http://dx.doi.org/10.1007/s00454-003-0005-8.

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Schurmann, Achill, and Frank Vallentin. "Computational Approaches to Lattice Packing and Covering Problems." Discrete & Computational Geometry 35, no. 1 (October 12, 2005): 73–116. http://dx.doi.org/10.1007/s00454-005-1202-2.

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Dissertations / Theses on the topic "Geometric Covering and Packing"

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Song, Yongqiang. "Improved Approximation Algorithms for Geometric Packing Problems With Experimental Evaluation." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4355/.

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Geometric packing problems are NP-complete problems that arise in VLSI design. In this thesis, we present two novel algorithms using dynamic programming to compute exactly the maximum number of k x k squares of unit size that can be packed without overlap into a given n x m grid. The first algorithm was implemented and ran successfully on problems of large input up to 1,000,000 nodes for different values. A heuristic based on the second algorithm is implemented. This heuristic is fast in practice, but may not always be giving optimal times in theory. However, over a wide range of random data this version of the algorithm is giving very good solutions very fast and runs on problems of up to 100,000,000 nodes in a grid and different ranges for the variables. It is also shown that this version of algorithm is clearly superior to the first algorithm and has shown to be very efficient in practice.
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Bezdek, Andras. "Packing and covering problems /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487266691095136.

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Chen, Zhibin, and 陳智斌. "On various packing and covering problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43085520.

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Chen, Zhibin. "On various packing and covering problems." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B43085520.

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Nielsen, Torben Noerup. "Combinatorial Bin Packing Problems." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187536.

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In the past few years, there has been a strong and growing interest in evaluating the expected behavior of what we call combinatorial bin packing problems. A combinatorial bin packing problem consists of a number of items of various sizes and value ratios (value per unit of size) along with a collection of bins of fixed capacity into which the items are to be packed. The packing must be done in such a way that the sum of the sizes of the items into a given bin does not exceed the capacity of that bin. Moreover, an item must either be packed into a bin in its entirety or not at all: this "all or nothing" requirement is why these problems are characterized as being combinatorial. The objective of the packing is to optimize a given criterion Junction. Here optimize means either maximize or minimize, depending on the problem. We study two problems that fit into this framework: the Knapsack Problem and the Minimum Sum of Squares Problem. Both of these problems are known to be in the class of NP-hard problems and there is ample reason to suspect that these problems do not admit of efficient exact solution. We obtain results concerning the performance of heuristics under the assumption that the inputs are random samples from some distribution. For the Knapsack Problem, we develop four heuristics, two of which are on-line and two off-line. All four heuristics are shown to be asymptotically optimal in expectation when the item sizes and value ratios are assumed to be independent and uniform. One heuristic is shown to be asymptotically optimal in expectation when the item sizes are uniformly distributed and the value ratios are exponentially distributed. The amount of time required by these heuristics is no more than proportional to the amount of time required to sort the items in order of nonincreasing value ratios. For the Minimum Sum of Squares Problem, we develop two heuristics, both of which are off-line. Both of these heuristics are shown to be asymptotically optimal in expectation when the sizes of the items input are assumed uniformly distributed.
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Stardom, John. "Metaheuristics and the search for covering and packing arrays." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ61608.pdf.

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Pasha, Arfath. "Geometric bin packing algorithm for arbitrary shapes." [Gainesville, Fla.] : University of Florida, 2003. http://purl.fcla.edu/fcla/etd/UFE0000907.

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Chang, Engder. "Neural computing for minimum set covering and gate-packing problems." Case Western Reserve University School of Graduate Studies / OhioLINK, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=case1056655652.

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許眞眞 and Zhenzhen Xu. "A min-max theorem on packing and covering cycles in graphs." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31226966.

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Xu, Zhenzhen. "A min-max theorem on packing and covering cycles in graphs /." Hong Kong : University of Hong Kong, 2002. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25155301.

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Books on the topic "Geometric Covering and Packing"

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Convegno, italiano di geometria integrale probabilità geometriche e. corpi convessi (4th 1994 Bari Italy). IV Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi: Bari, 2-5 maggio 1994. Palermo: Sede della società, 1995.

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Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi (5th 1995 Milan, Italy). V Convegno italiano di geometria integrale, probabilità geometriche e corpi convessi: Milano, 19-22 aprile 1995. Palermo: Sede della società, 1996.

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Rogers, C. A. Packing and covering. Cambridge: Cambridge University Press, 2008.

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Böröczky, K. Finite packing and covering. Cambridge, UK: Cambridge University Press, 2004.

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service), SpringerLink (Online, ed. The Kepler Conjecture: The Hales-Ferguson Proof. New York, NY: Springer Science+Business Media, LLC, 2011.

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Combinatorial optimization: Packing and covering. Philadelphia: Society for Industrial and Applied Mathematics, 2001.

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1951-, Cohen G., ed. Covering codes. Amsterdam: Elsevier, 1997.

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1943-, Itoh Yoshiaki, and ebrary Inc, eds. Random sequential packing of cubes. Singapore: World Scientific, 2011.

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Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. Providence, Rhode Island: American Mathematical Society, 2014.

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Gerardus Joannes Maria Van Wee. Covering codes, perfect codes, and codes from algebraic curves. Helmond [Netherlands]: Wibro Dissertatiedrukkerij, 1991.

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Book chapters on the topic "Geometric Covering and Packing"

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Croft, Hallard T., Kenneth J. Falconer, and Richard K. Guy. "Packing and Covering." In Unsolved Problems in Geometry, 107–30. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-0963-8_5.

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Chekuri, Chandra, Sariel Har-Peled, and Kent Quanrud. "Fast LP-based Approximations for Geometric Packing and Covering Problems." In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 1019–38. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611975994.62.

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Ashok, Pradeesha, Aniket Basu Roy, and Sathish Govindarajan. "Local Search Strikes Again: PTAS for Variants of Geometric Covering and Packing." In Lecture Notes in Computer Science, 25–37. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62389-4_3.

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Yakovlev, Sergiy. "Configuration Spaces of Geometric Objects with Their Applications in Packing, Layout and Covering Problems." In Advances in Intelligent Systems and Computing, 122–32. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26474-1_9.

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Blinovsky, Volodia. "Covering and Packing." In Asymptotic Combinatorial Coding Theory, 41–61. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6193-4_3.

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Diestel, Reinhard. "Matching Covering and Packing." In Graph Theory, 35–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53622-3_2.

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Diestel, Reinhard. "Matching Covering and Packing." In Graph Theory, 35–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-642-14279-6_2.

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Mitchell, Joseph S. B., and Supantha Pandit. "Packing and Covering with Segments." In WALCOM: Algorithms and Computation, 198–210. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39881-1_17.

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Karakostas, George. "Fractional Packing and Covering Problems." In Encyclopedia of Algorithms, 778–82. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-2864-4_149.

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Karakostas, George. "Fractional Packing and Covering Problems." In Encyclopedia of Algorithms, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-27848-8_149-2.

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Conference papers on the topic "Geometric Covering and Packing"

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Azar, Yossi, Umang Bhaskar, Lisa Fleischer, and Debmalya Panigrahi. "Online Mixed Packing and Covering." In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973105.6.

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Gadouleau, Maximilien, and Zhiyuan Yan. "Packing and covering properties of subspace codes." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205292.

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Srinivasan, Aravind. "Improved approximations of packing and covering problems." In the twenty-seventh annual ACM symposium. New York, New York, USA: ACM Press, 1995. http://dx.doi.org/10.1145/225058.225138.

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Ene, Alina, Sariel Har-Peled, and Benjamin Raichel. "Geometric packing under non-uniform constraints." In the 2012 symposuim. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2261250.2261253.

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Young, N. E. "Sequential and parallel algorithms for mixed packing and covering." In Proceedings 42nd IEEE Symposium on Foundations of Computer Science. IEEE, 2001. http://dx.doi.org/10.1109/sfcs.2001.959930.

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Koufogiannakis, Christos, and Neal E. Young. "Beating Simplex for Fractional Packing and Covering Linear Programs." In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07). IEEE, 2007. http://dx.doi.org/10.1109/focs.2007.4389519.

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Koufogiannakis, Christos, and Neal E. Young. "Beating Simplex for Fractional Packing and Covering Linear Programs." In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07). IEEE, 2007. http://dx.doi.org/10.1109/focs.2007.62.

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Azar, Yossi, Niv Buchbinder, T.-H. Hubert Chan, Shahar Chen, Ilan Reuven Cohen, Anupam Gupta, Zhiyi Huang, et al. "Online Algorithms for Covering and Packing Problems with Convex Objectives." In 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2016. http://dx.doi.org/10.1109/focs.2016.24.

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Benko, Attila, Gyorgy Dosa, and Zsolt Tuza. "Bin Packing/Covering with Delivery, solved with the evolution of algorithms." In 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA). IEEE, 2010. http://dx.doi.org/10.1109/bicta.2010.5645312.

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Mount, David, and Ruth Silverman. "Algorithms for covering and packing and applications to CAD/CAM (abstract only)." In the 15th annual conference. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/322917.323100.

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Reports on the topic "Geometric Covering and Packing"

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Balas, E., G. Cornuejols, and J. N. Hooker. Covering, Packing and Logical Inference. Fort Belvoir, VA: Defense Technical Information Center, October 1993. http://dx.doi.org/10.21236/ada274314.

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