Privacy preserving clustering with constraints
The $k$-center problem is a classical combinatorial optimization problem which asks to find $k$ centers such that the maximum distance of any input point in a set $P$ to its assigned center is minimized. The problem allows for elegant $2$-approximations. However, the situation becomes significantly...
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| creator | Rösner, Clemens Schmidt, Melanie |
| description | The $k$-center problem is a classical combinatorial optimization problem
which asks to find $k$ centers such that the maximum distance of any input
point in a set $P$ to its assigned center is minimized. The problem allows for
elegant $2$-approximations. However, the situation becomes significantly more
difficult when constraints are added to the problem. We raise the question
whether general methods can be derived to turn an approximation algorithm for a
clustering problem with some constraints into an approximation algorithm that
respects one constraint more. Our constraint of choice is privacy: Here, we are
asked to only open a center when at least $\ell$ clients will be assigned to
it. We show how to combine privacy with several other constraints. |
| doi_str_mv | 10.48550/arxiv.1802.02497 |
| format | Article |
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which asks to find $k$ centers such that the maximum distance of any input
point in a set $P$ to its assigned center is minimized. The problem allows for
elegant $2$-approximations. However, the situation becomes significantly more
difficult when constraints are added to the problem. We raise the question
whether general methods can be derived to turn an approximation algorithm for a
clustering problem with some constraints into an approximation algorithm that
respects one constraint more. Our constraint of choice is privacy: Here, we are
asked to only open a center when at least $\ell$ clients will be assigned to
it. We show how to combine privacy with several other constraints.</description><identifier>DOI: 10.48550/arxiv.1802.02497</identifier><language>eng</language><subject>Computer Science - Computational Complexity</subject><creationdate>2018-02</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1802.02497$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1802.02497$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Rösner, Clemens</creatorcontrib><creatorcontrib>Schmidt, Melanie</creatorcontrib><title>Privacy preserving clustering with constraints</title><description>The $k$-center problem is a classical combinatorial optimization problem
which asks to find $k$ centers such that the maximum distance of any input
point in a set $P$ to its assigned center is minimized. The problem allows for
elegant $2$-approximations. However, the situation becomes significantly more
difficult when constraints are added to the problem. We raise the question
whether general methods can be derived to turn an approximation algorithm for a
clustering problem with some constraints into an approximation algorithm that
respects one constraint more. Our constraint of choice is privacy: Here, we are
asked to only open a center when at least $\ell$ clients will be assigned to
it. We show how to combine privacy with several other constraints.</description><subject>Computer Science - Computational Complexity</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjsOwjAQRVE3FAhYABXZQMI4Dh67RIifhAQFfTRxHLAEAdkhwO75Vu9WT4exIYckU5MJjMk_XJtwBWkCaaaxy5Kddy2ZZ3T1NljfuvoQmdMtNNZ_8u6aY2QudWg8uboJfdap6BTs4L89tl_M97NVvNku17PpJiaJGCOkGmVqSBvCkitdgsVKcTKVFlhAyYVCrgisqTKpBbxLQ5lRQYWSIEWPjX63X3B-9e5M_pl_4PkXLl4u5D4S</recordid><startdate>20180207</startdate><enddate>20180207</enddate><creator>Rösner, Clemens</creator><creator>Schmidt, Melanie</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20180207</creationdate><title>Privacy preserving clustering with constraints</title><author>Rösner, Clemens ; Schmidt, Melanie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-7029762ca9ca7d189d0e7f81acf937b0d138718a0ecf46930a0e90d4abab86063</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Computer Science - Computational Complexity</topic><toplevel>online_resources</toplevel><creatorcontrib>Rösner, Clemens</creatorcontrib><creatorcontrib>Schmidt, Melanie</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Rösner, Clemens</au><au>Schmidt, Melanie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Privacy preserving clustering with constraints</atitle><date>2018-02-07</date><risdate>2018</risdate><abstract>The $k$-center problem is a classical combinatorial optimization problem
which asks to find $k$ centers such that the maximum distance of any input
point in a set $P$ to its assigned center is minimized. The problem allows for
elegant $2$-approximations. However, the situation becomes significantly more
difficult when constraints are added to the problem. We raise the question
whether general methods can be derived to turn an approximation algorithm for a
clustering problem with some constraints into an approximation algorithm that
respects one constraint more. Our constraint of choice is privacy: Here, we are
asked to only open a center when at least $\ell$ clients will be assigned to
it. We show how to combine privacy with several other constraints.</abstract><doi>10.48550/arxiv.1802.02497</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Complexity |
| title | Privacy preserving clustering with constraints |
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