Approximating the Distortion
Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demon...
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| creator | Hall, Alexander Papadimitriou, Christos |
| description | Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demonstrating that, when the distortion is large, it is hard to approximate within large factors, even for 1-dimensional point sets. We also introduce additive distortion, and show that it can be easily approximated within a factor of two. |
| doi_str_mv | 10.1007/11538462_10 |
| format | Conference Proceeding |
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P.</contributor><creatorcontrib>Hall, Alexander</creatorcontrib><creatorcontrib>Papadimitriou, Christos</creatorcontrib><title>Approximating the Distortion</title><title>Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques</title><description>Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demonstrating that, when the distortion is large, it is hard to approximate within large factors, even for 1-dimensional point sets. We also introduce additive distortion, and show that it can be easily approximated within a factor of two.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Flows in networks. Combinatorial problems</subject><subject>Operational research and scientific management</subject><subject>Operational research. 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Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Flows in networks. Combinatorial problems</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hall, Alexander</creatorcontrib><creatorcontrib>Papadimitriou, Christos</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hall, Alexander</au><au>Papadimitriou, Christos</au><au>Trevisan, Luca</au><au>Chekuri, Chandra</au><au>Jansen, Klaus</au><au>Rolim, José D. P.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Approximating the Distortion</atitle><btitle>Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques</btitle><date>2005</date><risdate>2005</risdate><spage>111</spage><epage>122</epage><pages>111-122</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540282396</isbn><isbn>3540282394</isbn><eisbn>9783540318743</eisbn><eisbn>3540318747</eisbn><abstract>Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demonstrating that, when the distortion is large, it is hard to approximate within large factors, even for 1-dimensional point sets. We also introduce additive distortion, and show that it can be easily approximated within a factor of two.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11538462_10</doi><tpages>12</tpages></addata></record> |
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| ispartof | Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques, 2005, p.111-122 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_17115837 |
| source | Springer Books |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Computer science control theory systems Exact sciences and technology Flows in networks. Combinatorial problems Operational research and scientific management Operational research. Management science Theoretical computing |
| title | Approximating the Distortion |
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