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134
Viewdependent simplification of arbitrary polygonal environments
, 1997
"... Hierarchical dynamic simplification (HDS) is a new approach to the problem of simplifying arbitrary polygonal environments. HDS operates dynamically, retessellating the scene continuously as the user’s viewing position shifts, and adaptively, processing the entire database without first decomposing ..."
Abstract

Cited by 286 (15 self)
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vertex cluster occupies less than a userspecified amount of the screen, all vertices within that cluster are collapsed together and degenerate polygons filtered out. HDS maintains an active list of visible polygons for rendering. Since frametoframe movements typically involve small changes
MaterialDiscontinuity Preserving Progressive Mesh Using VertexCollapsing Simplification
"... Abstract: Level Of Detail (LOD) modelling or mesh reduction has been found useful in interactive walkthrough applications. Progressive meshing techniques based on edge or triangle collapsing have been recognised useful in continuous LOD, progressive refinement, and progressive transmission. We prese ..."
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present a vertexcollapsing mesh reduction scheme that effectively takes shape and feature preserving as well as materialdiscontinuity preserving into account, and produces a progressive mesh which generally has more vertices collapsed between adjacent levels of detail than methods based on edgecollapsing
Vertex routing models
, 906
"... Abstract. A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The longterm flow of information is governed by cyclic attractors, allowing to define a measure ..."
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Cited by 1 (0 self)
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of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed. PACS numbers: 89.75.Hc, 02.10.Ox, 87.23.Ge, 89.75.FbVertex
Mesh Collapse Compression
 In Proceedings of SIBGRAPI’99
, 1999
"... We present a novel algorithm for encoding the topology of triangular meshes. A sequence of edge contract and divide operations collapses the entire mesh into a single vertex. This implicitly creates a tree with weighted edges. The weights are vertex degrees and capture the topology of the unlabele ..."
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Cited by 3 (0 self)
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We present a novel algorithm for encoding the topology of triangular meshes. A sequence of edge contract and divide operations collapses the entire mesh into a single vertex. This implicitly creates a tree with weighted edges. The weights are vertex degrees and capture the topology
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 ..."
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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
Collapsing the Classifying SpaceHistory
"... vertex and infinitely many cells in each positive dimension. “Collapsed ” it to quotient complex with only two cells in each positive dimension. History ◮ (Brown–Geoghegan, 1984) Had cell complex X with one vertex and infinitely many cells in each positive dimension. “Collapsed ” it to quotient comp ..."
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vertex and infinitely many cells in each positive dimension. “Collapsed ” it to quotient complex with only two cells in each positive dimension. History ◮ (Brown–Geoghegan, 1984) Had cell complex X with one vertex and infinitely many cells in each positive dimension. “Collapsed ” it to quotient
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
Metric Geometry and Collapsibility
, 2012
"... Cheeger’s finiteness theorem bounds the number of diffeomorphism types of manifolds with bounded curvature, diameter and volume; the Hadamard–Cartan theorem, as popularized by Gromov, shows the contractibility of all nonpositively curved simply connected metric length spaces. We establish a discret ..."
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that all triangulations of Sd are exponentially many.) (4) If a vertextransitive simplicial complex is CAT(0) with the equilateral flat metric, then it is a simplex. (This connects metric geometry with the evasiveness conjecture.) (5) The space of phylogenetic trees is collapsible. (This connects discrete
VertexRounding a ThreeDimensional Polyhedral Subdivision
 Discrete Comput. Geom
, 1997
"... Let P be a polyhedral subdivision in R 3 with a total of n faces. We show that there is an embedding oe of the vertices, edges, and facets of P into a subdivision Q, where every vertex coordinate of Q is an integral multiple of 2 \Gammadlog 2 n+2e . For each face f of P , the Hausdorff distance ..."
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Cited by 20 (0 self)
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Let P be a polyhedral subdivision in R 3 with a total of n faces. We show that there is an embedding oe of the vertices, edges, and facets of P into a subdivision Q, where every vertex coordinate of Q is an integral multiple of 2 \Gammadlog 2 n+2e . For each face f of P , the Hausdorff distance
Subexponential Parameterized Algorithms Collapse the Whierarchy (Extended Abstract)
, 2001
"... It is shown that for essentially all MAX SNPhard optimization problems finding exact solutions in subexponential time is not possible unless W [1] = FPT . In particular, we show that O(2 o(k) p(n)) parameterized algorithms do not exist for Vertex Cover, Max Cut, Max cSat, and a number of pr ..."
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Cited by 54 (3 self)
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It is shown that for essentially all MAX SNPhard optimization problems finding exact solutions in subexponential time is not possible unless W [1] = FPT . In particular, we show that O(2 o(k) p(n)) parameterized algorithms do not exist for Vertex Cover, Max Cut, Max cSat, and a number
Results 1  10
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