12,366 Hits in 7.5 sec

Breaking Quadratic Time for Small Vertex Connectivity and an Approximation Scheme [article]

Danupon Nanongkai, Thatchaphol Saranurak, Sorrachai Yingchareonthawornchai
2021 arXiv   pre-print
no vertex connectivity algorithms are faster than O(n^2) time even for k=4 and m=O(n).  ...  Vertex connectivity a classic extensively-studied problem. Given an integer k, its goal is to decide if an n-node m-edge graph can be disconnected by removing k vertices.  ...  For exact vertex connectivity, we have k 2 ≤ n/4 ≤ m/4. For generality, we denote k 2 ≤ m/c. We use c = 1 + ǫ for the approximate vertex connectivity, and c = 4 for exact version.  ... 
arXiv:1904.04453v3 fatcat:uqq74zwglnc7niijnrq56djtbu

Breaking quadratic time for small vertex connectivity and an approximation scheme

Danupon Nanongkai, Thatchaphol Saranurak, Sorrachai Yingchareonthawornchai
2019 Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019  
no vertex connectivity algorithms are faster than O (n 2 ) time even for k = 4 and m = O (n).  ...  Vertex connectivity a classic extensively-studied problem. Given an integer k, its goal is to decide if an n-node m-edge graph can be disconnected by removing k vertices.  ...  For undirected approximate vertex connectivity, we first sparsify the graph in O (m) time. Let m ′ be the number of edges of the sparsified graph.  ... 
doi:10.1145/3313276.3316394 dblp:conf/stoc/NanongkaiSY19 fatcat:7u4vgvtfv5affiskdvp2oujftq

On a semi-implicit numerical method for the surface diffusion equation for triangulated surfaces

Yu. D. Efremenko
2021 Sibirskie Elektronnye Matematicheskie Izvestiya  
In addition, an algorithm of re-triangulation of surfaces was developed to handle singularities that appear during surface evolution.  ...  A number of numerical solutions for dierent initial surfaces is presented.  ...  Its only limitation is that in the break neighbourhood the calculations have to be performed with a small interval to process the rupture in time.  ... 
doi:10.33048/semi.2021.18.104 fatcat:dls47scbyjbqxf6h2mpz3yv6u4

Safe Approximation and Its Relation to Kernelization [chapter]

Jiong Guo, Iyad Kanj, Stefan Kratsch
2012 Lecture Notes in Computer Science  
We introduce a notion of approximation, called safe approximation, for minimization problems that are subset problems.  ...  We then study the relation between safe approximation and kernelization.  ...  The authors would like to thank Bart Jansen for suggesting the nice example used in the proof of Theorem 4.  ... 
doi:10.1007/978-3-642-28050-4_14 fatcat:2c7xqcqavrh7jae74ms2ndbowe

Exact cancellation of quadratic divergences in top condensation models

Andreas Blumhofer
1995 Nuclear Physics B  
We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model.  ...  Quadratic divergences appear at each order 1/N_c since fermionic and bosonic contributions are of different order 1/N_c.  ...  Model can be many orders of magnitude smaller than in other breaking schemes.  ... 
doi:10.1016/0550-3213(94)00563-t fatcat:zaqewysemfabncpulw3bqdzp4m

Propagators and phase structure of Nf=2 and Nf=2+1 QCD

Christian S. Fischer, Jan Luecker
2013 Physics Letters B  
We discuss the resulting thermal mass of the unquenched gluon propagator and extract order parameters for the chiral and deconfinement transition from the quarks.  ...  We investigate the phase structure of QCD at finite temperature and chemical potential by solving a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagator.  ...  ACKNOWLEDGEMENTS We thank Michael Buballa, Jens Braun, Leo Fister, Daniel Müller, Jan Pawlowski, Bernd-Jochen Schaefer, Lorenz von Smekal and Jochen Wambach for fruitful discussions.  ... 
doi:10.1016/j.physletb.2012.11.054 fatcat:egt3krhdqze5vj32b2dhopgyj4

Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs

Surender Baswana, Telikepalli Kavitha
2010 SIAM journal on computing (Print)  
We present a simple, novel and generic scheme for all-pairs approximate shortest paths.  ...  An estimateδ (u, v) u, v). Computing all-pairs small stretch distances efficiently (both in terms of time and space) is a well-studied problem in graph algorithms.  ...  The first author is very thankful to Max-Planck Institute for computer science, Saarbruecken, Germany for providing an excellent and inspirational research atmosphere.  ... 
doi:10.1137/080737174 fatcat:d5ofwojusjeibda5nlatzhebde

New renormalization group equations and the naturalness problem

Grigorii Pivovarov
2010 Physical Review D  
Looking for an observable manifestation of the so-called unnaturalness of scalar fields we introduce a seemingly new set of differential equations for connected Green functions.  ...  These equations describe the momentum dependence of the Green functions and are close relatives to the previously known renormalization group equations.  ...  Still, the error is less than 20%, and the approximation again improves at very small m because at zero m the error vanishes.  ... 
doi:10.1103/physrevd.81.076007 fatcat:g4fo564azzc6pegdrcp7mccl5a

Approximate Distance Oracles with Improved Preprocessing Time [article]

Christian Wulff-Nilsen
2011 arXiv   pre-print
Our results break the quadratic preprocessing time bound of Baswana and Kavitha for all $k\geq 6$ and improve the $O(kmn^{1/k})$ time bound of Thorup and Zwick except for very sparse graphs and small $  ...  Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\geq 1$, we show that for some universal constant $c$, a $(2k-1)$-approximate distance  ...  We see that Theorem 2 breaks the quadratic time bound of Baswana and Kavitha [2] when k ≥ 6.  ... 
arXiv:1109.4156v1 fatcat:idmtsb5yurd5bnjb3jszeh4f3y

Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective [article]

Max Hering, Vincent Noculak, Francesco Ferrari, Yasir Iqbal, Johannes Reuther
2021 arXiv   pre-print
Using various parton ansätze for quantum spin liquids, dimerized and nematic states our results indicate a tendency for lattice symmetry breaking in the ground state.  ...  The first part of our analysis is based on an enhanced parton mean-field approach which takes into account fluctuation effects from renormalized vertex functions.  ...  We use an iterative scheme in which we start with ξ − = 0 and ξ + = ∆ ξ as well as some fixed n ω and n k .  ... 
arXiv:2110.08160v1 fatcat:t7t5je63y5dyhkepvjshlfnzei

Parallel Graph Decompositions Using Random Shifts [article]

Gary L. Miller, Richard Peng, Shen Chen Xu
2013 arXiv   pre-print
We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between.  ...  As with earlier works on tree embedding, we will pick a special vertex in each piece, and use the distance to the farthest vertex from it as an estimate for the diameter.  ...  The search takes one unit of time to propagate across an edge, and each such time steps can be performed in parallel over all vertices.  ... 
arXiv:1307.3692v1 fatcat:rwclrutzgrefrejwdqhsesvh2a

The sound of an evolving floating sculpture [article]

Benjamin Seibold, Yossi Farjoun
2012 arXiv   pre-print
The surface is approximated by a triangulation, and we present a robust approach to approximate the normal directions and the mean curvature.  ...  Commissioned by MIT's in-house artist Jane Philbrick, we evolve an abstract 2D surface (resembling Marta Pan's 1961 "Sculpture Flottante I") under mean curvature, all the while calculating the eigenmodes  ...  Acknowledgments The authors would like to express their gratitude to Jane Philbrick (MIT Center for Advanced Visual Studies), who approached us mathematicians with an open mind for a joint project, for  ... 
arXiv:1201.4621v1 fatcat:ofnjjjco6zhsjgetsa5k2qex4e

Skeleton Based As-Rigid-As-Possible Volume Modeling [article]

Shaoting Zhang, Andrew Nealen, Dimitris Metaxas
2010 Eurographics State of the Art Reports  
In our experiments, we show that the rotations are natural and volumes are roughly kept. The system achieves real time performance for surface meshes with 5k vertices.  ...  Shape deformation and editing are important for animation and game design.  ...  This approach computes a natural rotation for each vertex and approximately preserves the edge length and the volume.  ... 
doi:10.2312/egsh.20101038 fatcat:rjsidkhn4bghppv6b3vhpebcj4

A quadratic motion-based object-oriented video codec

Y. Yemez, B. Sankur, E. Anarım
2000 Signal processing. Image communication  
A pixel tG J 3¹ is an admissible vertex if and only if it complies with De"nition 4.3, and moreover d(tG J , s J ))D .  ...  vertex candidates, are ordered sets, which is required for a computationally e$cient algorithm.  ...  The quadratic transform used for object motion modeling, relates the coordinates of an object pixel between two consecutive image frames at time instances t!1 and t. (This generic time di!  ... 
doi:10.1016/s0923-5965(99)00017-x fatcat:p5n47xg5l5alrcex25izrzd2ou

Dynamical vertex mass generation and chiral symmetry breaking on the light front

Matthias Burkardt
1998 Physical Review D, Particles and fields  
While the kinetic mass is basically generated by a zero-mode induced counter-term, the vertex mass is generated dynamically by infinitesimally small, but nonzero, momenta.  ...  Naively, helicity flip amplitudes for fermions seem to vanish in the chiral limit of light-front QCD, which would make it nearly impossible to generate a small pion mass in this framework.  ...  , and one cannot consider it an approximation to QCD or a phenomenological model for QCD.  ... 
doi:10.1103/physrevd.58.096015 fatcat:kh4u56pwv5dkrh5ojvprrg5kfi
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