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

פרסום מחקרי: פרק בספר / בדוח / בכנס › פרסום בספר כנס › ביקורת עמיתים

תקציר

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.

שפה מקורית	אנגלית
כותר פרסום המארח	Approximation, Randomization, and Combinatorial Optimization
כותר משנה של פרסום המארח	Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
מוציא לאור	Springer Verlag
עמודים	242-256
מספר עמודים	15
מסת"ב (מודפס)	9783540742074
מזהי עצם דיגיטלי (DOIs)	https://doi.org/10.1007/978-3-540-74208-1_18
סטטוס פרסום	פורסם - 2007
אירוע	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, ארצות הברית משך הזמן: 20 אוג׳ 2007 → 22 אוג׳ 2007

סדרות פרסומים

שם	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
כרך	4627 LNCS
ISSN (מודפס)	0302-9743
ISSN (אלקטרוני)	1611-3349

כנס

כנס	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
מדינה/אזור	ארצות הברית
עיר	Princeton, NJ
תקופה	20/08/07 → 22/08/07

גישה למסמך

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

קבצים וקישורים אחרים

Link to publication in Scopus

פורמט ציטוט ביבליוגרפי

Mendel, M., & Naor, A. (2007). Maximum gradient embeddings and monotone clustering. ב- Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings (עמודים 242-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); כרך 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. עמודים 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",

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Mendel, M & Naor, A 2007, Maximum gradient embeddings and monotone clustering. ב- 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), כרך 4627 LNCS, Springer Verlag, עמודים 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, ארצות הברית, 20/08/07. 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. עמוד 242-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); כרך 4627 LNCS).

פרסום מחקרי: פרק בספר / בדוח / בכנס › פרסום בספר כנס › ביקורת עמיתים

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Mendel M, Naor A. Maximum gradient embeddings and monotone clustering. ב- Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag. 2007. עמוד 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

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