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293
Listing triangles
 In Automata, Languages, and Programming  41st International Colloquium, ICALP 2014
"... Abstract. We present new algorithms for listing triangles in dense and sparse graphs. The running time of our algorithm for dense graphs is Õ(nω + n3(ω−1)/(5−ω)t2(3−ω)/(5−ω)), and the running time of the algorithm for sparse graphs is Õ(m2ω/(ω+1) + m3(ω−1)/(ω+1)t(3−ω)/(ω+1)), where n is the numbe ..."
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Cited by 9 (0 self)
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Abstract. We present new algorithms for listing triangles in dense and sparse graphs. The running time of our algorithm for dense graphs is Õ(nω + n3(ω−1)/(5−ω)t2(3−ω)/(5−ω)), and the running time of the algorithm for sparse graphs is Õ(m2ω/(ω+1) + m3(ω−1)/(ω+1)t(3−ω)/(ω+1)), where n
Reducing 3XOR to listing triangles, an exposition
, 2011
"... The 3SUM problem asks if there are three integers a, b, c summing to 0 in a given set of n integers of magnitude poly(n). This problem can be easily solved in time Õ(n2). (Throughout this note, Õ and ˜ Ω hide subpolynomial factors no(1).) It seems natural to believe that this problem also requires t ..."
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SUM to the problem of listing triangles of a graph.[Pǎt10] In this note we present this reduction by Pǎtra¸scu but for a variant of the 3SUM problem which we call 3XOR. The problem 3XOR is like 3SUM except that integer summation is replaced with bitwise xor. So one can think of 3XOR as asking if a
Comparing top k lists
 In Proceedings of the ACMSIAM Symposium on Discrete Algorithms
, 2003
"... Motivated by several applications, we introduce various distance measures between “top k lists.” Some of these distance measures are metrics, while others are not. For each of these latter distance measures, we show that they are “almost ” a metric in the following two seemingly unrelated aspects: ( ..."
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Cited by 272 (4 self)
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Motivated by several applications, we introduce various distance measures between “top k lists.” Some of these distance measures are metrics, while others are not. For each of these latter distance measures, we show that they are “almost ” a metric in the following two seemingly unrelated aspects
DepthPresorted Triangle Lists
"... selection realtime depthsorted renderings input triangles offline preprocess depthpresorted triangle list (triangles & halfspaces) input static model Figure 1: Our offline preprocessing algorithm produces a depthpresorted triangle list from a static 3D input model. The list contains copie ..."
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selection realtime depthsorted renderings input triangles offline preprocess depthpresorted triangle list (triangles & halfspaces) input static model Figure 1: Our offline preprocessing algorithm produces a depthpresorted triangle list from a static 3D input model. The list contains
ROAMing Terrain: Realtime Optimally Adapting Meshes
, 1997
"... Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and groundbased aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, viewdepend ..."
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Cited by 287 (10 self)
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additional performance optimizations: incremental triangle stripping and prioritycomputation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution
List coloring trianglefree hypergraphs
, 2013
"... Abstract A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g with u, v ∈ e, v, w ∈ f , w, u ∈ g and {u, v, w} ∩ e ∩ f ∩ g = ∅. Johansson We provide a common generalization of both these results for rank 3 hypergraphs (edges have size 2 or 3). Our resu ..."
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Cited by 1 (1 self)
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Abstract A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g with u, v ∈ e, v, w ∈ f , w, u ∈ g and {u, v, w} ∩ e ∩ f ∩ g = ∅. Johansson We provide a common generalization of both these results for rank 3 hypergraphs (edges have size 2 or 3). Our
On Triangles and Flow
 Special Section on Software Agents”. in Electronic Markets
, 1996
"... : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 131 List of Figures 1.1 Interpretation of a gridoblique shear . . . . . . . . . . . . . . . . . . . . 3 1.2 Acute cell and refined cell with twice the minimum angle. . . . . . . . . . 7 3.1 Linear variation of the data ..."
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Cited by 10 (0 self)
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: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 131 List of Figures 1.1 Interpretation of a gridoblique shear . . . . . . . . . . . . . . . . . . . . 3 1.2 Acute cell and refined cell with twice the minimum angle. . . . . . . . . . 7 3.1 Linear variation
by congruent triangles
, 2001
"... Abstract. We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure poin ..."
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Abstract. We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure
PDTL: Parallel and Distributed Triangle Listing for Massive Graphs
, 2015
"... Abstract — This paper presents the first distributed triangle listing algorithm with provable CPU, I/O, Memory, and Network bounds. Finding all triangles (3cliques) in a graph has numerous applications for density and connectivity metrics. The majority of existing algorithms for massive graphs are ..."
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Abstract — This paper presents the first distributed triangle listing algorithm with provable CPU, I/O, Memory, and Network bounds. Finding all triangles (3cliques) in a graph has numerous applications for density and connectivity metrics. The majority of existing algorithms for massive graphs
3SUM, 3XOR, Triangles
, 2013
"... We show that if one can solve 3SUM on a set of size n in time n1+ɛ then one can list t triangles in a graph with m edges in time Õ(m1+ɛt1/3+ɛ ′ ) for any ɛ ′> 0. This is a reversal of Pǎtra¸scu’s reduction from 3SUM to listing triangles (STOC ’10). We then reexecute both Pǎtra¸scu’s reduction an ..."
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Cited by 3 (0 self)
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We show that if one can solve 3SUM on a set of size n in time n1+ɛ then one can list t triangles in a graph with m edges in time Õ(m1+ɛt1/3+ɛ ′ ) for any ɛ ′> 0. This is a reversal of Pǎtra¸scu’s reduction from 3SUM to listing triangles (STOC ’10). We then reexecute both Pǎtra¸scu’s reduction
Results 1  10
of
293