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Cut Tree Construction from Massive Graphs [article]

Takuya Akiba, Yoichi Iwata, Yosuke Sameshima, Naoto Mizuno, Yosuke Yano
2016 arXiv   pre-print
The 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.  ... 
arXiv:1609.08723v1 fatcat:ohntmqicxjerbnijwz73a67cia

Loop-Level Double-Copy for Massive Quantum Particles [article]

John Joseph M. Carrasco, Ingrid A. Vazquez-Holm
2020 arXiv   pre-print
We find that factorization and the color-kinematics duality are sufficient principles to entirely bootstrap these calculations, allowing us to 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 →  ... 
arXiv:2010.13435v2 fatcat:s3ipfy2pujejtmmcxtsmchpmhm

Extracting Einstein from the Loop-Level Double-Copy [article]

John Joseph M. Carrasco, Ingrid A. Vazquez-Holm
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] ).  ... 
arXiv:2108.06798v1 fatcat:pvc5rhhhtfbtnd7mizuz34dqju

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

K. Madduri, D.A. Bader
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.  ... 
doi:10.1109/ipdps.2009.5161060 dblp:conf/ipps/MadduriB09 fatcat:zmhf354mznharab6dkuzqrj55q

Graph sketches

Kook Jin Ahn, Sudipto Guha, Andrew McGregor
2012 Proceedings of the 31st symposium on Principles of Database Systems - PODS '12  
When processing 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.  ... 
doi:10.1145/2213556.2213560 dblp:conf/pods/AhnGM12 fatcat:3xaqt3j5lvhy7koj2vlvvlncaq

Adaptive Massively Parallel Algorithms for Cut Problems

MohammadTaghi Hajiaghayi, Marina Knittel, Jan Olkowski, Hamed Saleh
2022 Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures  
We study the Weighted Min 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.  ... 
doi:10.1145/3490148.3538576 fatcat:4o7tglrdong6ffntilm3uswajy

Adaptive Massively Parallel Algorithms for Cut Problems [article]

MohammadTaghi Hajiaghayi, Marina Knittel, Jan Olkowski, Hamed Saleh
2022 arXiv   pre-print
We study the Weighted Min 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.  ... 
arXiv:2205.14101v1 fatcat:iyufc4yfqncdpkjlhbwmisyu4e

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-'.  ... 

Snowmass White Paper: the Double Copy and its Applications [article]

Tim Adamo, John Joseph M. Carrasco, Mariana Carrillo-González, Marco Chiodaroli, Henriette Elvang, Henrik Johansson, Donal O'Connell, Radu Roiban, Oliver Schlotterer
2022 arXiv   pre-print
We gratefully acknowledge the following for valuable feedback in the 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.  ... 
arXiv:2204.06547v1 fatcat:erf2pkfcl5f7rkvj7itudy7znq

Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions

Dirk Kreimer, Andrea Velenich
2012 Letters in Mathematical Physics  
In the 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  ... 
doi:10.1007/s11005-012-0589-y fatcat:mz3zupfjyffebnnya4axfghsea

Large-order perturbation theory in infrared-unstable superrenormalizable field theories

John M. Cornwall
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 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.  ... 
doi:10.1103/physrevd.55.6209 fatcat:bvn4wjq6fbhpnaakgrvxbrbwvm

On-shell recursion relations for generic integrands [article]

Rutger H. Boels, Hui Luo
2016 arXiv   pre-print
Apart 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  ... 
arXiv:1610.05283v1 fatcat:wuunkxbv25atlollbzxse4kdsa

Analyzing Graph Structure via Linear Measurements [chapter]

Kook Jin Ahn, Sudipto Guha, Andrew McGregor
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
There is already extensive literature on processing 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.  ... 
doi:10.1137/1.9781611973099.40 dblp:conf/soda/AhnGM12 fatcat:os72cpdtl5bzjdbcolmbb6resi

The Duality Between Color and Kinematics and its Applications [article]

Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, Radu Roiban
2019 arXiv   pre-print
[194] which also verified it against the direct 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.  ... 
arXiv:1909.01358v1 fatcat:vox5fwaatzbjhp6peunp3vb4ga

Partitioning and Handling Massive Models for Interactive Collision Detection

A. Wilson, E. Larsen, D. Manocha, M. C. Lin
1999 Computer graphics forum (Print)  
We present a new algorithm using overlap 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.  ... 
doi:10.1111/1467-8659.00352 fatcat:tqxrlkthb5dadpz6qfag757yyu
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