arXiv subjects

Christian Sommer

Publications and source records attributed to Christian Sommer.

23 records · Page 2Linked to original sources

arXiv2011

More Compact Oracles for Approximate Distances in Planar Graphs

Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. In FOCS'01, Thorup introduced approximate distance oracles for planar graphs. He proved that, for any eps>0 and for any planar graph on n nodes, there exists a (1+eps)-approximate distance oracle using space O(n eps^{-1} log n) such that approximate distance queries can be answered in time O(1/eps). Ten years later, we give the first improvements on the space-querytime tradeoff for planar graphs. * We give the first oracle having a space-time product with subquadratic dependency on 1/eps. For space ~O(n log n) we obtain query time ~O(1/eps) (assuming polynomial edge weights). The space shows a doubly logarithmic dependency on 1/eps only. We believe that the dependency on eps may be almost optimal. * For the case of moderate edge weights (average bounded by polylog(n), which appears to be the case for many real-world road networks), we hit a "sweet spot," improving upon Thorup's oracle both in terms of eps and n. Our oracle uses space ~O(n log log n) and it has query time ~O(log log log n + 1/eps). (Asymptotic notation in this abstract hides low-degree polynomials in log(1/eps) and log*(n).)

cs.DS↗

arXiv2011

Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs

A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of εand independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(n lg^2 n). However, our constructions have slower query times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our linear-space results, we can in fact ensure, for any delta > 0, that the space required is only 1 + delta times the space required just to represent the graph itself.

cs.DS↗

arXiv2010

Velocity-selected molecular pulses produced by an electric guide

Electrostatic velocity filtering is a technique for the production of continuous guided beams of slow polar molecules from a thermal gas. We extended this technique to produce pulses of slow molecules with a narrow velocity distribution around a tunable velocity. The pulses are generated by sequentially switching the voltages on adjacent segments of an electric quadrupole guide synchronously with the molecules propagating at the desired velocity. This technique is demonstrated for deuterated ammonia (ND$_{3}$), delivering pulses with a velocity in the range of $20-100\,\rm{m/s}$ and a relative velocity spread of $(16\pm 2)\,%$ at FWHM. At velocities around $60\,\rm{m/s}$, the pulses contain up to $10^6$ molecules each. The data are well reproduced by Monte-Carlo simulations, which provide useful insight into the mechanisms of velocity selection.

physics.chem-ph↗

arXiv2008

Collisional effects in the formation of cold guided beams of polar molecules

High fluxes of cold polar molecules are efficiently produced by electric guiding and velocity filtering. Here, we investigate different aspects of the beam formation. Variations of the source parameters such as density and temperature result in characteristic changes in the guided beam. These are observed in the velocity distribution of the guided molecules as well as in the dependence of the signal of guided molecules on the trapping electric field. A model taking into account velocity-dependent collisional losses of cold molecules in the region close to the nozzle accurately reproduces this behavior. This clarifies an open question on the parameter dependence of the detected signal and gives a more detailed understanding of the velocity filtering and guiding process.

physics.chem-ph↗

arXiv2008

Continuous guided beams of slow and internally cold polar molecules

We describe the combination of buffer-gas cooling with electrostatic velocity filtering to produce a high-flux continuous guided beam of internally cold and slow polar molecules. In a previous paper (L.D. van Buuren et al., arXiv:0806.2523v1) we presented results on density and state purity for guided beams of ammonia and formaldehyde using an optimized set-up. Here we describe in more detail the technical aspects of the cryogenic source, its operation, and the optimization experiments that we performed to obtain best performance. The versatility of the source is demonstrated by the production of guided beams of different molecular species.

physics.chem-ph↗