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The Unique Games Conjecture, integrality gap for cut problems and embeddability of negative type metrics into `1
 In Proc. 46th IEEE Symp. on Foundations of Comp. Sci
, 2005
"... In this paper we disprove the following conjecture due to Goemans [17] and Linial [25] (also see [5, 27]): “Every negative type metric embeds into `1 with constant distortion. ” We show that for every δ> 0, and for large enough n, there is an npoint negative type metric which requires distortion ..."
Abstract

Cited by 180 (13 self)
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“integrality gap instances ” for the respective problems. Towards this, we first construct an integrality gap instance for a natural SDP relaxation of Unique Games. Then, we “simulate ” the PCP reduction, and “translate ” the integrality gap instance of Unique Games to integrality gap instances
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into ℓ1∗
"... ar ..."
Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding
 IEEE TRANS. ON INFORMATION THEORY
, 1999
"... We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing informationembedding rate, mini ..."
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Cited by 495 (15 self)
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We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing informationembedding rate
SDP integrality gaps with local ℓ1embeddability
 In Proc. 50 th IEEE FOCS
, 2009
"... We construct integrality gap instances for SDP relaxation of the MAXIMUM CUT and the SPARSEST CUT problems. If the triangle inequality constraints are added to the SDP, then the SDP vectors naturally define an npoint negative type metric where n is the number of vertices in the problem instance. Ou ..."
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Cited by 13 (4 self)
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We construct integrality gap instances for SDP relaxation of the MAXIMUM CUT and the SPARSEST CUT problems. If the triangle inequality constraints are added to the SDP, then the SDP vectors naturally define an npoint negative type metric where n is the number of vertices in the problem instance
Obliq  A language with distributed scope
, 1995
"... computation. An Obliq computation may involve multiple threads of control within an address space, multiple address spaces on a machine, heterogeneous machines over a local network, and multiple networks over the Internet. Obliq objects have state and are local to a site. Obliq computations can roam ..."
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Cited by 433 (12 self)
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computation. An Obliq computation may involve multiple threads of control within an address space, multiple address spaces on a machine, heterogeneous machines over a local network, and multiple networks over the Internet. Obliq objects have state and are local to a site. Obliq computations can
On the geometry and cohomology of some simple Shimura varieties
, 1999
"... This paper has twin aims. On the one hand we prove the local Langlands conjecture for GL n over a padic field. On the other hand in many cases we are able to identify the action of the decomposition group at a prime of bad reduction on the ladic cohomology of the "simple" Shimura varieti ..."
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Cited by 341 (19 self)
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varieties studied by Kottwitz in [Ko4]. These two problems go hand in hand. The local Langlands conjecture is one of those hydra like conjectures which seems to grow as it gets proved. However the generally accepted formulation seems to be the following (see [He2]). Let K be a finite extension of Q p . Fix
The Cut Cone, L¹ Embeddability, Complexity . . .
, 1990
"... A finite metric (or more properly semimetric) on n points is a nonnegative vector d = (dij) 1 ≤ i < j ≤ n that satisfies the triangle inequality: dij ≤ dik + d jk. The L 1 (or Manhattan)distance x  − y 1  between two vectors x = (xi) and y = (yi) in R m is given by x − y 1  = Σ xi − yi. ..."
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. A metric d is L 1≤i≤m 1 − embeddable if there exist vectors z1, z2,..., zn in R m for some m, such that dij = z i − z j 1  for 1 ≤ i < j ≤ n. A cut metric is a metric with all distances zero or one and corresponds to the incidence vector of a cut in the complete graph on n vertices. The cut
ON THE GEOMETRY OF METRICS EMBEDDABLE IN THE REAL Line
, 2009
"... For a fixed finite set {1,..., n}, we consider the set of metrics for which the metric space can be isometrically embedded in the real line. The convex hull of those metrics, Qn, and its closure Qn are the main objects of this paper. We first study structural properties of Qn showing how the set o ..."
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of metrics is contained in this convex set and characterize all unbounded onedimensional extreme subsets of Qn combinatorially. Second, and mainly, we give a combinatorial characterization of the set of unbounded edges of Qn. As a simple byproduct, we obtain that Qn is closed if and only if n ≤ 3. We note
Results 1  10
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