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 algo-rithm for sparse graphs is Õ(m2ω/(ω+1) + m3(ω−1)/(ω+1)t(3−ω)/(ω+1)), where n

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 bit-wise xor. So one can think of 3XOR as asking if a

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

selection real-time depth-sorted renderings input triangles off-line preprocess depth-presorted triangle list (triangles & half-spaces) input static model Figure 1: Our off-line preprocessing algorithm produces a depth-presorted triangle list from a static 3D input model. The list contains

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

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

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 131 List of Figures 1.1 Interpretation of a grid-oblique shear . . . . . . . . . . . . . . . . . . . . 3 1.2 Acute cell and refined cell with twice the minimum angle. . . . . . . . . . 7 3.1 Linear variation

Abstract. We give a new classification of tilings of the 2-dimensional 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

Abstract — This paper presents the first distributed triangle listing algorithm with provable CPU, I/O, Memory, and Network bounds. Finding all triangles (3-cliques) in a graph has numerous applications for density and connectivity metrics. The majority of existing algorithms for massive graphs

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 re-execute both Pǎtra¸scu’s reduction