Local versus Global Properties of Metric Spaces Extended abstract

被引：6

作者：

Arora, Sanjeev ^{[1
]}

Lovasz, Laszlo ^{[2
,3
]}

Newman, Ilan ^{[4
]}

Rabani, Yuval ^{[5
]}

Rabinovich, Yuri ^{[4
]}

Vempala, Santosh ^{[6
]}

机构：

[1] Princeton Univ, Dept Comp Sci, Princeton, NJ 08544 USA

[2] Microsoft Res, Redmond, WA 98052 USA

[3] Lorand Univ, Dept Comp Sci, Budapest, Hungary

[4] Univ Haifa, Dept Comp Sci, IL-31905 Haifa, Israel

[5] Technion, Dept Comp Sci, IL-32000 Haifa, Israel

[6] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

PROCEEDINGS OF THE SEVENTHEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS | 2006年

关键词：

D O I：

10.1145/1109557.1109563

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Motivated by applications in combinatorial optimization, we initiate a study of the extent to which the global properties of a metric space (especially, embeddability in l(1) with low distortion) are determined by the properties of small subspaces. We note connections to similar issues studied already in Ramsey theory, complexity theory (especially PCPs), and property testing. We prove both upper bounds and lower bounds on the distortion of embedding locally constrained metrics into various target spaces.

引用

页码：41 / +

页数：3

共 50 条

[41] On the local behavior of mappings of metric spaces
Sevost’yanov E.A.
Skvortsov S.A.
Journal of Mathematical Sciences, 2020, 244 (1) : 47 - 55
[42] Local multifractal analysis in metric spaces
Kaenmaki, Antti
Rajala, Tapio
Suomala, Ville
NONLINEARITY, 2013, 26 (08) : 2157 - 2173
[43] CONCERNING LOCAL SEPARABILITY IN METRIC SPACES
TREYBIG, LB
DUKE MATHEMATICAL JOURNAL, 1962, 29 (01) : 125 - &
[44] LOCAL CONDITIONS FOR GLOBAL CONVERGENCE OF GRADIENT FLOWS AND PROXIMAL POINT SEQUENCES IN METRIC SPACES
Dello Schiavo, Lorenzo
Maas, Jan
Pedrotti, Francesco
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 377 (06) : 3779 - 3804
[45] Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces
Doric, Dragan
Kadelburg, Zoran
Radenovic, Stojan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 1927 - 1932
[46] Meir-Keeler-type conditions in abstract metric spaces
Kadelburg, Zoran
Radenovic, Stojan
APPLIED MATHEMATICS LETTERS, 2011, 24 (08) : 1411 - 1414
[47] DIFFERENTIAL LIPSCHITZIANNESS TESTS ON ABSTRACT QUASI-METRIC SPACES
TURINICI, M
ACTA MATHEMATICA HUNGARICA, 1983, 41 (1-2) : 93 - 100
[48] FIXED POINT RESULTS FOR COUPLINGS ON ABSTRACT METRIC SPACES AND AN APPLICATION
Aydi, Hassen
Felhi, Abdelbasset
Afshari, H.
Marasi, H. R.
Isik, H.
JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS, 2018, 9 (02): : 57 - 67
[49] Abstract metric spaces and Sehgal-Guseman-type theorems
Pavlovic, Mirjana
Radenovic, Stojan
Radojevic, Slobodan
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (03) : 865 - 872
[50] ABSTRACT METRIC SPACES AND CARISTI-NGUYEN-TYPE THEOREMS
Kadelburg, Zoran
Radenovic, Stojan
Simic, Suzana
FILOMAT, 2011, 25 (03) : 111 - 124

← 1 2 3 4 5 →