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2.
Let
and
be two collections of a total ofn (possibly partially defined) bivariate, algebraic functions of constant maximum degree. The minimization diagrams of
are the planar maps obtained by the xy-projections of the lower envelopes of
, respectively. We show that the combinatiorial complexity of the overlay of the minimization diagrams of
and of
is O(n2+ɛ), for any ɛ>0. This result has several applications: (i) a near-quadratic upper bound on the complexity of the region in
3-space enclosed between the lower envelope of one such collection of functions and the upper envelope of another collection;
(ii) an efficient and simple divide-and-conquer algorithm for constructing lower envelopes in three dimensions; and (iii)
a near-quadratic upper bound on the complexity of the space of all plane transversals of a collection of simply shaped convex
sets in three dimensions.
Work on this paper by the first author was supported by National Science Foundation Grant CCR-93-01259 and an NYI award. Work
on this paper by the second author was supported by the Netherlands’ Organization for Scientific Research (NWO) and partially
supported by ESPRIT Basic Research Action No. 6546 (project PROMotion). His current address is Department of Computer Science,
Postech, San 31, Hyoja-Dong, Pohang, Kyungbuk 790–784, South Korea. Email: otfried@vision.postech.ac.kr. Work on this paper
by the third author was supported by NSF Grant CCR-91-22103, by a Max-Planck Research Award, and by grants from the U.S.-Israeli
Binational Science Foundation the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F.,
the German-Israeli Foundation for Scientific Research and Development. 相似文献
3.
We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. They can also be used to show the presence of bound entanglement in the thermal states of several spin models. 相似文献
4.
J.D. Schwarzkopf C.T. Crowe J.J. Riley S. Wetchagarun P. Dutta 《International Journal of Multiphase Flow》2009
This study focuses on understanding how the presence of particles, in homogeneous turbulence decay, affects the dissipation of dissipation coefficient within the volume averaged dissipation transport equation. In developing this equation, the coefficient for dissipation of dissipation was assumed to be the sum of the single phase coefficient and an additional coefficient that is related to the effects of the dispersed phase. Direct numerical simulation was used to isolate the effect of stationary particles in homogeneous turbulent decay at low Reynolds numbers (ReL = 3.3 and 12.5). The particles were positioned at each grid point and modeled as point forces and a comparison was made between a 643 and 1283 domain. The results show that the dissipation of dissipation coefficient correlates well with a dimensionless parameter called the momentum coupling factor. 相似文献
5.
Otfried Cheong Xavier Goaoc Andreas Holmsen Sylvain Petitjean 《Discrete and Computational Geometry》2008,39(1-3):194-212
We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ
d
. In particular, we show that a family of n≥2d disjoint unit balls in ℝ
d
has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ
d
admits a line transversal if any subfamily of size 4d−1 admits a transversal.
Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc
acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR). 相似文献
6.
We present an approach to characterize genuine multiparticle entanglement by using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated by using semidefinite programing and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponential improvement compared with existing schemes. 相似文献
7.
We introduce a new type of randomized incremental algorithms. Contrary to standard randomized incremental algorithms, theselazy randomized incremental algorithms are suited for computing structures that have a “nonlocal” definition. In order to analyze
these algorithms we generalize some results on random sampling to such situations. We apply our techniques to obtain efficient
algorithms for the computation of single cells in arrangements of segments in the plane, single cells in arrangements of triangles
in space, and zones in arrangements of hyperplanes.
This research was supported by the Netherlands' Organization for Scientific Research (NWO) and partially by the ESPRIT III
Basic Research Action 6546 (PROMotion). Part of this research was done while K.D. was visiting Utrecht University. 相似文献
8.
Pankaj K. Agarwal Herbert Edelsbrunner Otfried Schwarzkopf Emo Welzl 《Discrete and Computational Geometry》1991,6(1):407-422
We present an algorithm to compute a Euclidean minimum spanning tree of a given setS ofN points inE
d
in timeO(F
d
(N,N) log
d
N), whereF
d
(n,m) is the time required to compute a bichromatic closest pair amongn red andm green points inE
d
. IfF
d
(N,N)=Ω(N
1+ε), for some fixed ɛ>0, then the running time improves toO(F
d
(N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected timeO((nm logn logm)2/3+m log2
n+n log2
m) inE
3, which yields anO(N
4/3 log4/3
N) expected time, algorithm for computing a Euclidean minimum spanning tree ofN points inE
3. Ind≥4 dimensions we obtain expected timeO((nm)1−1/([d/2]+1)+ε+m logn+n logm) for the bichromatic closest pair problem andO(N
2−2/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive ɛ.
The first, second, and fourth authors acknowledge support from the Center for Discrete Mathematics and Theoretical Computer
Science (DIMACS), a National Science Foundation Science and Technology Center under NSF Grant STC 88-09648. The second author's
work was supported by the National Science Foundation under Grant CCR-8714565. The third author's work was supported by the
Deutsche Forschungsgemeinschaft under Grant A1 253/1-3, Schwerpunktprogramm “Datenstrukturen und effiziente Algorithmen”.
The last two authors' work was also partially supported by the ESPRIT II Basic Research Action of the EC under Contract No.
3075 (project ALCOM). 相似文献
9.
We present an extension of Bardeen's model for the formation of Cooper pairs that includes a schematic representation of a nonlocal interaction. The model is exactly solvable and we investigate its Hartree-Fock, BCS and Hartree-Fock-Bogoliubov approximations focusing upon the role and significance of the particle number dispersions. 相似文献
10.