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797
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
Abstract

Cited by 1189 (15 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
ABSTRACT
"... This paper presents a new error bound simplification algorithm for complex geometric models. A lower polygon count approximation of the input model is generated by performing edge collapse operations. The collapse vertex is constrained to lie within a localised tolerance volume built around the edge ..."
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the edge collapse neighbourhood. This constraint ensures that all points on the simplified surface are within a user specified distance from the surface after the previous edge collapse.
Structure and tie strengths in mobile communication networks
 Proc. Natl. Acad. Sci. (USA
, 2007
"... We examine the communication patterns of millions of anonymized mobile phone users. Based on call records, we construct a communication network where vertices are subscribers and edge weights are defined as aggregated duration of calls, reflecting the strengths of social ties between callers. We obs ..."
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Cited by 239 (13 self)
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We examine the communication patterns of millions of anonymized mobile phone users. Based on call records, we construct a communication network where vertices are subscribers and edge weights are defined as aggregated duration of calls, reflecting the strengths of social ties between callers. We
Fast and Memory Efficient Polygonal Simplification
, 1998
"... Conventional wisdom says that in order to produce highquality simplified polygonal models, one must retain and use information about the original model during the simplification process. We demonstrate that excellent simplified models can be produced without the need to compare against information ..."
Abstract

Cited by 157 (7 self)
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from the original geometry while performing local changes to the model. We use edge collapses to perform simplification, as do a number of other methods. We select the position of the new vertex so that the original volume of the model is maintained and we minimize the pertriangle change in volume
On regular neighbourhoods
 Proc. London Math. Soc
, 1964
"... IN (11) J. H. C. Whitehead introduced the theory of regular neighbourhoods, which has become a basic tool in combinatorial topology. We extend the theory in three ways. First we relativize the concept, and introduce the regular neighbourhood N of X mod Y in M, where X and Y are two compact polyhedr ..."
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Cited by 2 (0 self)
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polyhedra in the manifold M, satisfying a certain condition called linkcollapsibility. We prove existence and uniqueness theorems. The idea is that N should be a neighbourhood of XY, but should avoid Y as much as possible. The notion is extremely useful in practice, and is illustrated by the following
Mesh parameterization based on edge collapse *
, 2008
"... Abstract: Parameterizations that use mesh simplification to build the base domain always adopt the vertex removal scheme. This paper applies edge collapse to constructing the base domain instead. After inducing the parameterization of the original mesh over the base domain, new algorithms map the ne ..."
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Abstract: Parameterizations that use mesh simplification to build the base domain always adopt the vertex removal scheme. This paper applies edge collapse to constructing the base domain instead. After inducing the parameterization of the original mesh over the base domain, new algorithms map
Cavitation Bubble Collapse in Neighbourhood of a Solid Boundary, " Journal
"... 5 Shutler, N. D., and Mesler, R. B., "A Photographic Study of the ..."
ANF: A Fast and Scalable Tool for Data Mining in Massive Graphs
 NTERNATIONAL CONFERENCE ON KNOWLEDGE DISCOVERY AND DATA MINING
, 2002
"... Graphs are an increasingly important data source, with such important graphs as the Internet and the Web. Other familiar graphs include CAD circuits, phone records, gene sequences, city streets, social networks and academic citations. Any kind of relationship, such as actors appearing in movies, can ..."
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Cited by 121 (18 self)
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differences in movie appearance patterns? At its core, ANF is based on a fast and memoryefficient approach for approximating the complete "neighbourhood function" for a graph. For the Internet graph (268K nodes), ANF's highlyaccurate approximation is more than 700 times faster than the exact
Surface quasigeostrophic dynamics
, 1995
"... The dynamics of quasigeostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to twodimensional flow, with surface temperature playing the role of vorticity, but a different relationshi ..."
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Cited by 117 (3 self)
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relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an elliptical vortex; the startup vortex shed by flow over a mountain; the instability of temperature filaments; the ‘edge
Satisfiability Allows No Nontrivial Sparsification Unless The PolynomialTime Hierarchy Collapses
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 38 (2010)
, 2010
"... Consider the following twoplayer communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small ..."
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Cited by 56 (2 self)
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that the polynomialtime hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for ǫ = 0. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several
Results 1  10
of
797