Biased Range Trees

Dujmović, Vida; Howat, John; Morin, Pat

doi:10.1137/1.9781611973068.54

Cited by 9 publications

(14 citation statements)

References 15 publications

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“…High energy neutrinos have been extensively studied by the IceCube collaboration. 8 They have recently observed two double cascade events [60], consistent with ν τ . This would imply a neutrino flavor ratio ν e : ν µ : ν τ ∼ 1.05 : 1.35 : 0.6, consistent with 1 : 1 : 1 expected from a pion decay source after taking oscillations into account.…”

Section: Cosmic Raysmentioning

confidence: 79%

Conference Summary and Outlook: Particle Physics Past, Present, and Future

Langacker¹

2019

Proceedings of the 39th International Conference on High Energy Physics — PoS(ICHEP2018)

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The combination of these experimental probes established the basic structure of the SU(2) × U(1) model, constrained small deviations from many types of new physics, confirmed the program of renormalization, correctly predicted the approximate values of the t and (less accuratedly) Higgs masses, and indicated an approximate unification of the gauge couplings (including the QCD coupling) at a very high energy scale. (The gauge unification is more successful in the supersymmetric extension.) [Figure 3]• The observation of neutrino mass and mixing effects, 2 established in atmospheric neutrino oscillations in 1998 [28] (but with strong indications earlier from Solar neutrinos). It is still not certain whether the masses are Dirac or Majorana.• The observation of the Brout-Englert-Higgs (BEH) or "Higgs" boson by the ATLAS and CMS collaborations in 2012. Quantum Chromodynamics (QCD)The strong interaction part of the Standard Model is QCD [Figure 4], which was developed in the early 1970s (e.g., [29]). QCD is a gauge theory based on SU(3). It is essentially the unique renormalizable field theory consistent with the experimental information available at the time. Principal ingredients and developments included:• Deep inelastic ep scattering [17] and e + e − annihilation experiments at SLAC, which established spin-1/2 partons (quarks) and color.• The notions of asymptotic freedom [30,31], infrared slavery, and color confinement.• The observation of the gluon at DESY in 1979.

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Section: Cosmic Raysmentioning

confidence: 79%

Conference Summary and Outlook: Particle Physics Past, Present, and Future

Langacker¹

2019

Proceedings of the 39th International Conference on High Energy Physics — PoS(ICHEP2018)

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“…A preliminary version of the results in the current paper have appeared in the Proceedings of the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA 2009) [19]. Since then, Afshani et al [1] have discovered a general approach to distribution-sensitive geometric data structures that has many applications.…”

Section: New Resultsmentioning

confidence: 98%

Biased Range Trees

2010

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A data structure, called a biased range tree, is presented that preprocesses a set S of n points in R 2 and a query distribution D for 2-sided orthogonal range counting queries (a.k.a. dominance counting queries). The expected query time for this data structure, when queries are drawn according to D, matches, to within a constant factor, that of the optimal comparison tree for S and D. The memory and preprocessing requirements of the data structure are O(n log n).

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“…Alstrup, Brodal, and Reuhe [4] further showed that range reporting in R 3 can be done with O(n log 1+ε n) space and O(log n + k) query time in the RAM model. More recently, Dujmović, Howat, and Morin [15] developed a data structure called a biased range tree which, assuming that 2-sided ranges are drawn from a probability distribution, can perform 2-sided range counting queries efficiently. Afshani, Barbay, and Chan [1] generalized this result, showing the existence of many instance-optimal algorithms.…”

Section: Prior Workmentioning

confidence: 99%

“…Range searching is a classic problem that has received much attention in the Computational Geometry literature (e.g., see [2,3,7,10,12,15,19,21,22,25]). In what is perhaps the simplest form of range searching, called orthogonal range reporting, we are given a rectangular, axis-aligned query range R and our goal is to report the points p contained inside R for a given point set, S.…”

Section: Introductionmentioning

confidence: 99%

Priority Range Trees

Goodrich

Strash

2010

Algorithms and Computation

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We describe a data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points. Let S be a set of n points in the plane, where each point p in S is assigned a weight w(p) that is polynomial in n, and define the rank of p to be r(p) = log w(p) . Then the priority range tree can be used to report all points in a three-or four-sided query range R with rank at least log w in time O(logW /w + k), and report k highestrank points in R in time O(log log n + logW /w + k), where W = ∑ p∈S w(p), w is the smallest weight of any point reported, and k is the output size. All times assume the standard RAM model of computation. If the query range of interest is three sided, then the priority range tree occupies O(n) space, otherwise O(n log n) space is used to answer four-sided queries. These queries are motivated by the Weber-Fechner Law, which states that humans perceive and interpret data on a logarithmic scale.

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Biased Range Trees

Cited by 9 publications

References 15 publications

Conference Summary and Outlook: Particle Physics Past, Present, and Future

Conference Summary and Outlook: Particle Physics Past, Present, and Future

Biased Range Trees

Priority Range Trees

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