Maximum gradient embeddings and monotone clustering

Manor Mendel; Assaf Naor

doi:10.1007/978-3-540-74208-1_18

Maximum gradient embeddings and monotone clustering

Manor Mendel, Assaf Naor

מדעי המחשב

نتاج البحث: فصل من :كتاب / تقرير / مؤتمر › منشور من مؤتمر › مراجعة النظراء

ملخص

Let (X, d_x) be an n-point metric space. We show that there exists a distribution & over non-contractive embeddings into trees f : X → T such that for every x ∈ X, E_D [max _v∈X\(x) d_T(f(x), f(y))/d_X(x, y)] < C(log n)₂ where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.

اللغة الأصلية	الإنجليزيّة
عنوان منشور المضيف	Approximation, Randomization, and Combinatorial Optimization
العنوان الفرعي لمنشور المضيف	Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
ناشر	Springer Verlag
الصفحات	242-256
عدد الصفحات	15
رقم المعيار الدولي للكتب (المطبوع)	9783540742074
المعرِّفات الرقمية للأشياء	https://doi.org/10.1007/978-3-540-74208-1_18
حالة النشر	نُشِر - 2007
الحدث	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, الولايات المتّحدة المدة: ٢٠ أغسطس ٢٠٠٧ → ٢٢ أغسطس ٢٠٠٧

سلسلة المنشورات

الاسم	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
مستوى الصوت	4627 LNCS
رقم المعيار الدولي للدوريات (المطبوع)	0302-9743
رقم المعيار الدولي للدوريات (الإلكتروني)	1611-3349

!!Conference

!!Conference	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
الدولة/الإقليم	الولايات المتّحدة
المدينة	Princeton, NJ
المدة	٢٠/٠٨/٠٧ → ٢٢/٠٨/٠٧

الوصول إلى المستند

10.1007/978-3-540-74208-1_18

الملفات والروابط الأخرى

Link to publication in Scopus

قم بذكر هذا

Mendel, M., & Naor, A. (2007). Maximum gradient embeddings and monotone clustering. في Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings (الصفحات 242-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); المجلد 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_18

Mendel, Manor ; Naor, Assaf. / Maximum gradient embeddings and monotone clustering. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. الصفحات 242-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Maximum gradient embeddings and monotone clustering",

abstract = "Let (X, dx) be an n-point metric space. We show that there exists a distribution & over non-contractive embeddings into trees f : X → T such that for every x ∈ X, ED [max v∈X\(x) dT(f(x), f(y))/dX(x, y)] < C(log n)2 where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.",

author = "Manor Mendel and Assaf Naor",

year = "2007",

doi = "10.1007/978-3-540-74208-1_18",

language = "אנגלית",

isbn = "9783540742074",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "242--256",

booktitle = "Approximation, Randomization, and Combinatorial Optimization",

address = "גרמניה",

note = "10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 ; Conference date: 20-08-2007 Through 22-08-2007",

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Mendel, M & Naor, A 2007, Maximum gradient embeddings and monotone clustering. في Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), المجلد 4627 LNCS, Springer Verlag, الصفحات 242-256, 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007, Princeton, NJ, الولايات المتّحدة, ٢٠/٠٨/٠٧. https://doi.org/10.1007/978-3-540-74208-1_18

Maximum gradient embeddings and monotone clustering. / Mendel, Manor; Naor, Assaf.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. صفحة 242-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); المجلد 4627 LNCS).

نتاج البحث: فصل من :كتاب / تقرير / مؤتمر › منشور من مؤتمر › مراجعة النظراء

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Mendel M, Naor A. Maximum gradient embeddings and monotone clustering. في Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag. 2007. صفحة 242-256. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74208-1_18

Maximum gradient embeddings and monotone clustering

ملخص

سلسلة المنشورات

!!Conference

الوصول إلى المستند

الملفات والروابط الأخرى

بصمة

قم بذكر هذا