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Cut Tree Construction from Massive Graphs
[article]

2016
*
arXiv
*
pre-print

The

arXiv:1609.08723v1
fatcat:ohntmqicxjerbnijwz73a67cia
*construction*of*cut**trees*(also known as Gomory-Hu*trees*) for a given*graph*enables the minimum-*cut*size of the original*graph*to be obtained for any pair of vertices. ... However, the crucial drawback with*cut**trees*is the computational cost of their*construction*. ... CONCLUSIONS In this paper, we have described a new algorithm for*constructing**cut**trees**from**massive*real-world*graphs*. ...##
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Loop-Level Double-Copy for Massive Quantum Particles
[article]

2020
*
arXiv
*
pre-print

We find that factorization and the color-kinematics duality are sufficient principles to entirely bootstrap these calculations, allowing us to

arXiv:2010.13435v2
fatcat:s3ipfy2pujejtmmcxtsmchpmhm
*construct*all contributions ultimately*from*the three-point ...*tree*-level amplitudes which are themselves entirely constrained by symmetry. ... l 1 ) 2 (a + l 1 ) 2 . (42) On the*tree*side of this*cut*, we get a product of the fourpoint*trees*with two*massive*scalars*from*the previous section, A 1-loop 4 (a m1 , b m1 , c m2 , d m2 )*cut*l 2 1 → ...##
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Extracting Einstein from the Loop-Level Double-Copy
[article]

2021
*
arXiv
*
pre-print

*from*propagating antisymmetric tensor and dilaton states even at

*tree*-level. ... We present a

*graph*-based approach that combines the method of maximal

*cuts*with double-copy

*construction*to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions ... The first examples of gravitational multi-loop

*cut*-

*construction*involved

*tree*-level

*cuts*built

*from*ordered gauge-theory

*cuts*by applying field theory KLT relations (see, e.g. [55] ). ...

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Compact graph representations and parallel connectivity algorithms for massive dynamic network analysis

2009
*
2009 IEEE International Symposium on Parallel & Distributed Processing
*

*Graph*-theoretic abstractions are extensively used to analyze

*massive*data sets. ... Temporal data streams

*from*socioeconomic interactions, social networking web sites, communication traffic, and scientific computing can be intuitively modeled as

*graphs*. ... Also, it is relatively simple to

*construct*the link-

*cut*

*tree*, given the network. ...

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Graph sketches

2012
*
Proceedings of the 31st symposium on Principles of Database Systems - PODS '12
*

When processing

doi:10.1145/2213556.2213560
dblp:conf/pods/AhnGM12
fatcat:3xaqt3j5lvhy7koj2vlvvlncaq
*massive*data sets, a core task is to*construct*synopses of the data. ... Our main result is a sketch-based sparsifier*construction*: we show that O̅ (nε -2 ) random linear projections of a*graph*on n nodes suffice to (1 + ε) approximate all*cut*values. ... Our work addresses the problem of*constructing*these synopses for*massive**graphs*. Specifically, we show how to*construct*such synopses given only linear projections of the input*graph*. ...##
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Adaptive Massively Parallel Algorithms for Cut Problems

2022
*
Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
*

We study the Weighted Min

doi:10.1145/3490148.3538576
fatcat:4o7tglrdong6ffntilm3uswajy
*Cut*problem in the Adaptive*Massively*Parallel Computation (AMPC) model. ... In the past decade, research on highly scalable algorithms has had significant impact on many*massive*systems. ... Our Contributions and Methods This work is the first to study the Adaptive*Massively*Parallel Computation (AMPC) model for Min*Cut*problems on*graphs*. ...##
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Adaptive Massively Parallel Algorithms for Cut Problems
[article]

2022
*
arXiv
*
pre-print

We study the Weighted Min

arXiv:2205.14101v1
fatcat:iyufc4yfqncdpkjlhbwmisyu4e
*Cut*problem in the Adaptive*Massively*Parallel Computation (AMPC) model. ... In the past decade, research on highly scalable algorithms has had significant impact on many*massive*systems. ...*cut*obtained*from*the Gomory-Hu*tree*. ...##
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Page 2765 of Mathematical Reviews Vol. , Issue 2004d
[page]

2004
*
Mathematical Reviews
*

Examples of properties studied include

*graph*colorability and existence of large cliques,*cuts*and bisections. ... Notice that Y may be obtained*from*%1;; by joining x and y exactly when F{x,y}=1. The main proof requires*constructing*conjugacies @; in AutI'¢, 20044:05184 such that 7; = 0;6;0-'. ...##
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Snowmass White Paper: the Double Copy and its Applications
[article]

2022
*
arXiv
*
pre-print

We gratefully acknowledge the following for valuable feedback in the

arXiv:2204.06547v1
fatcat:erf2pkfcl5f7rkvj7itudy7znq
*construction*of this white paper: Daniel Baumann, Justin Berman, Zvi Bern, Ji-Yian Du, Alex Edison, Michael Graesser, Daniel Green, ... For a*cut*between a six-point*tree*and a four-point*tree*of a four-fermion amplitude with one*cut*fermion and two*cut*gluon lines, the duality reduces the number of*cuts**from*24 to 6, cf. ... Now only four distinct*cuts*need be considered. A similar reduction holds for the*cut*between a six-point*tree*and a four-point*tree*. ...##
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Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions

2012
*
Letters in Mathematical Physics
*

In the

doi:10.1007/s11005-012-0589-y
fatcat:mz3zupfjyffebnnya4axfghsea
*massive*field theory the situation is more subtle. ... We find that*tree*level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. ... In the following we will see that the*cut*-*constructibility*of loop amplitudes*from**tree*amplitudes does not extend to the*massive*theory (8) due to the appearance of tadpole diagrams which hinder the application ...##
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Large-order perturbation theory in infrared-unstable superrenormalizable field theories

1997
*
Physical Review D, Particles and fields
*

At large external momentum p (or small mass M) and large order N one might expect perturbative bare skeleton

doi:10.1103/physrevd.55.6209
fatcat:bvn4wjq6fbhpnaakgrvxbrbwvm
*graphs*to behave roughly like N! ... The semi- classical Lipatov technique (which works only in the presence of a mass) is blind to this momentum dependence, so we proceed by direct summation of bare skeleton*graphs*. ... This gives the same*graph*in N + 1st order, but*constructed**from*a different*graph*at Nth order. ...##
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On-shell recursion relations for generic integrands
[article]

2016
*
arXiv
*
pre-print

Apart

arXiv:1610.05283v1
fatcat:wuunkxbv25atlollbzxse4kdsa
*from*a diagrammatic*construction*, at one loop order we provide a direct cross-check for box coefficients. ... Interestingly, at one loop our proposal can be related to a specific subset of all double unitarity*cuts*as well as*tree*-level poles by iterated recursion. ... One-loop 3-pt*construction*For three points, one starts*from*the*tree*-level amplitude involving two*massive*complex scalars [43] , A 3 (φ 1 , 1 + , 2 + , 3 − , φ 2 ) = − i 3|L / 1 (p / 1 + p / 2 )|3 ...##
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Analyzing Graph Structure via Linear Measurements
[chapter]

2012
*
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
*

There is already extensive literature on processing

doi:10.1137/1.9781611973099.40
dblp:conf/soda/AhnGM12
fatcat:os72cpdtl5bzjdbcolmbb6resi
*massive**graphs*in the data-stream model. ... of the original*graph*can be inferred*from*the sketch with high probability. ... Note that we are*constructing*a*tree*of*cuts*with a polynomial number of*cuts*. ...##
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The Duality Between Color and Kinematics and its Applications
[article]

2019
*
arXiv
*
pre-print

[194] which also verified it against the direct

arXiv:1909.01358v1
fatcat:vox5fwaatzbjhp6peunp3vb4ga
*construction**from*unitarity*cuts*. ... Looplevel amplitudes can of course be*constructed**from**tree*-level ones with unitarity methods. ... To relate the amplitude just*constructed*to the classical scattering of*massive*bodies it is necessary to focus on the classical kinematic regime. ...##
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Partitioning and Handling Massive Models for Interactive Collision Detection

1999
*
Computer graphics forum (Print)
*

We present a new algorithm using overlap

doi:10.1111/1467-8659.00352
fatcat:tqxrlkthb5dadpz6qfag757yyu
*graphs*for localizing the "regions of interest" within a*massive*model, thereby reducing runtime memory requirements. ... The overlap*graph*is computed off-line, pre-processed using*graph*partitioning algorithms, and modified on the fly as needed. ... We subdivide the geometry of an object using a k-D*tree**constructed*at the centers of its component polygons. This k-D*tree*subdivision is computed*from*building the scene*graph*. ...
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