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COARSE EMBEDDABILITY INTO BANACH SPACES
, 2008
"... The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse nonembeddability into ℓ2 implie ..."
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Cited by 4 (0 self)
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The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse nonembeddability into ℓ2
EMBEDDABILITY OF MULTIPLE CONES
, 706
"... Abstract. The main result of this paper is that if X is a Peano continuum such that its nth cone C n (X) embeds into R n+2 then X embeds into S 2. This solves a problem proposed by W. Rosicki. ..."
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Abstract. The main result of this paper is that if X is a Peano continuum such that its nth cone C n (X) embeds into R n+2 then X embeds into S 2. This solves a problem proposed by W. Rosicki.
Representing embeddability as set inclusion
 Journal of LMS (2nd series), No.185
, 1998
"... ABSTRACT. A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph’s endstructure. Using a combinatorial theorem of Shelah it is proved: The complexity of the class in ..."
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Cited by 7 (2 self)
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ABSTRACT. A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph’s endstructure. Using a combinatorial theorem of Shelah it is proved: The complexity of the class
On the Hardness of PointSet Embeddability?
"... Abstract. A pointset embedding of a plane graph G with n vertices on a set S of n points is a straightline drawing of G, where the vertices of G are mapped to distinct points of S. The problem of deciding whether a plane graph admits a pointset embedding on a given set of points is NPcomplete fo ..."
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Cited by 2 (0 self)
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Abstract. A pointset embedding of a plane graph G with n vertices on a set S of n points is a straightline drawing of G, where the vertices of G are mapped to distinct points of S. The problem of deciding whether a plane graph admits a pointset embedding on a given set of points is NP
HOMOTOPY INVARIANCE OF AFEMBEDDABILITY
, 2002
"... Abstract. We prove that AFembeddability is a homotopy invariant in the class of separable exact C ∗algebras. This work was inspired by Spielberg’s work on homotopy invariance of AFembeddability and Dadarlat’s serial works on AFembeddability of residually finite dimensional C ∗algebras. 1. ..."
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Abstract. We prove that AFembeddability is a homotopy invariant in the class of separable exact C ∗algebras. This work was inspired by Spielberg’s work on homotopy invariance of AFembeddability and Dadarlat’s serial works on AFembeddability of residually finite dimensional C ∗algebras. 1.
Embeddable Overlay Networks
, 2007
"... Internet RoundTripTimes (RTTs) exhibit widespread and persistent Triangle Inequality Violations (TIVs). It has been shown that TIVs are a natural consequence of the Internet’s routing structure and they degrade the embedding accuracy of any Internet coordinate systems based on RTTs. In this paper, ..."
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Cited by 6 (1 self)
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Internet RoundTripTimes (RTTs) exhibit widespread and persistent Triangle Inequality Violations (TIVs). It has been shown that TIVs are a natural consequence of the Internet’s routing structure and they degrade the embedding accuracy of any Internet coordinate systems based on RTTs. In this paper, we simulate a coordinate system in a hypothetical overlay environment where RTTs are measured with respect to overlay forwarding that has eliminated all the TIVs. The resulting coordinate system is much more accurate and the embedding accuracy is predictable and stable (under simulated node churn) than the existing techniques based on RTTs along paths chosen by native IP forwarding. We believe that this work helps to illustrate the detrimental effects of TIVs on Internet coordinate systems, and it suggests that high quality coordinate systems in the global Internet may be possible only with overlay forwarding.
SQL Anywhere: An Embeddable DBMS
"... We present an overview of the embeddability features of SQL Anywhere, a fullfunction relational database system designed for frontline business environments with minimal administration. SQL Anywhere supports features common to enterpriseclass database management systems, such as intraquery parall ..."
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We present an overview of the embeddability features of SQL Anywhere, a fullfunction relational database system designed for frontline business environments with minimal administration. SQL Anywhere supports features common to enterpriseclass database management systems, such as intra
On the Embeddability of Skeleta of Spheres
, 2008
"... We consider a generalization of the van KampenFlores Theorem and relate it to the longstanding gconjecture for simplicial spheres. 1 Introduction and results A wellknown result by van Kampen [26, 25] and by Flores [5] asserts that Theorem 1.1. The dskeleton of the (2d + 2)simplex does not embe ..."
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We consider a generalization of the van KampenFlores Theorem and relate it to the longstanding gconjecture for simplicial spheres. 1 Introduction and results A wellknown result by van Kampen [26, 25] and by Flores [5] asserts that Theorem 1.1. The dskeleton of the (2d + 2)simplex does not embed in the 2dsphere. The special case d = 1, which says that the complete graph on 5 vertices is
On the Embeddability of Random Walk Distances
"... Analysis of large graphs is critical to the ongoing growth of search engines and social networks. One class of queries centers around node affinity, often quantified by randomwalk distances between node pairs, including hitting time, commute time, andpersonalized PageRank (PPR). Despite the potenti ..."
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Analysis of large graphs is critical to the ongoing growth of search engines and social networks. One class of queries centers around node affinity, often quantified by randomwalk distances between node pairs, including hitting time, commute time, andpersonalized PageRank (PPR). Despite the potential of these “metrics, ” they are rarely, if ever, used in practice, largely due to extremely high computational costs. In this paper, we investigate methods to scalably and efficiently compute randomwalk distances, by “embedding ” graphs and distances into points and distances in geometric coordinate spaces. We show that while existing graph coordinate systems (GCS) can accurately estimate shortest path distances, they produce significant errors when embedding randomwalk distances. Based on our observations, we propose a new graph embedding system that explicitly accounts for pernode graph properties that affect random walk. Extensive experiments on a range of graphs show that our new approach can accurately estimate both symmetric and asymmetric randomwalk distances. Once a graph is embedded, our system can answer queries between any two nodes in 8 microseconds, orders of magnitude faster than existing methods. Finally, we show that our system produces estimates that can replace ground truth in applications with minimal impact on application output. 1.
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