673 research outputs found
Improved bounds and algorithms for graph cuts and network reliability
Karger (SIAM Journal on Computing, 1999) developed the first fully-polynomial
approximation scheme to estimate the probability that a graph becomes
disconnected, given that its edges are removed independently with probability
. This algorithm runs in time to obtain an
estimate within relative error .
We improve this run-time through algorithmic and graph-theoretic advances.
First, there is a certain key sub-problem encountered by Karger, for which a
generic estimation procedure is employed, we show that this has a special
structure for which a much more efficient algorithm can be used. Second, we
show better bounds on the number of edge cuts which are likely to fail. Here,
Karger's analysis uses a variety of bounds for various graph parameters, we
show that these bounds cannot be simultaneously tight. We describe a new graph
parameter, which simultaneously influences all the bounds used by Karger, and
obtain much tighter estimates of the cut structure of . These techniques
allow us to improve the runtime to , our results also
rigorously prove certain experimental observations of Karger & Tai (Proc.
ACM-SIAM Symposium on Discrete Algorithms, 1997). Our rigorous proofs are
motivated by certain non-rigorous differential-equation approximations which,
however, provably track the worst-case trajectories of the relevant parameters.
A key driver of Karger's approach (and other cut-related results) is a bound
on the number of small cuts: we improve these estimates when the min-cut size
is "small" and odd, augmenting, in part, a result of Bixby (Bulletin of the
AMS, 1974)
Analysis of pivot sampling in dual-pivot Quicksort: A holistic analysis of Yaroslavskiy's partitioning scheme
The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-015-0041-7The new dual-pivot Quicksort by Vladimir Yaroslavskiy-used in Oracle's Java runtime library since version 7-features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot Quicksort. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample. Surprisingly, dual-pivot Quicksort then needs more comparisons than a corresponding version of classic Quicksort, so it is clear that counting comparisons is not sufficient to explain the running time advantages observed for Yaroslavskiy's algorithm in practice. Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It turns out that the asymmetries in Yaroslavskiy's algorithm render pivots with a systematic skew more efficient than the symmetric choice. Moreover, we finally have a convincing explanation for the success of Yaroslavskiy's algorithm in practice: compared with corresponding versions of classic single-pivot Quicksort, dual-pivot Quicksort needs significantly less I/Os, both with and without pivot sampling.Peer ReviewedPostprint (author's final draft
Desorption of alkali atoms from 4He nanodroplets
The dynamics following the photoexcitation of Na and Li atoms located on the
surface of helium nanodroplets has been investigated in a joint experimental
and theoretical study. Photoelectron spectroscopy has revealed that excitation
of the alkali atoms via the (n+1) -> ns transition leads to the desorption of
these atoms. The mean kinetic energy of the desorbed atoms, as determined by
ion imaging, shows a linear dependence on excitation frequency. These
experimental findings are analyzed within a three-dimensional, time-dependent
density functional approach for the helium droplet combined with a Bohmian
dynamics description of the desorbing atom. This hybrid method reproduces well
the key experimental observables. The dependence of the observables on the
impurity mass is discussed by comparing the results obtained for the 6Li and
7Li isotopes. The calculations show that the desorption of the excited alkali
atom is accompanied by the creation of highly non-linear density waves in the
helium droplet that propagate at supersonic velocities
Space-Efficient DFS and Applications: Simpler, Leaner, Faster
The problem of space-efficient depth-first search (DFS) is reconsidered. A
particularly simple and fast algorithm is presented that, on a directed or
undirected input graph with vertices and edges, carries out a
DFS in time with bits of working memory, where is the
(total) degree of , for each , and . A slightly more complicated variant of the algorithm works in the same
time with at most bits. It is also shown that a DFS can
be carried out in a graph with vertices and edges in
time with bits or in time with either
bits or, for arbitrary integer , bits. These
results among them subsume or improve most earlier results on space-efficient
DFS. Some of the new time and space bounds are shown to extend to applications
of DFS such as the computation of cut vertices, bridges, biconnected components
and 2-edge-connected components in undirected graphs
Fluctuations of fragment observables
This contribution presents a review of our present theoretical as well as
experimental knowledge of different fluctuation observables relevant to nuclear
multifragmentation. The possible connection between the presence of a
fluctuation peak and the occurrence of a phase transition or a critical
phenomenon is critically analyzed. Many different phenomena can lead both to
the creation and to the suppression of a fluctuation peak. In particular, the
role of constraints due to conservation laws and to data sorting is shown to be
essential. From the experimental point of view, a comparison of the available
fragmentation data reveals that there is a good agreement between different
data sets of basic fluctuation observables, if the fragmenting source is of
comparable size. This compatibility suggests that the fragmentation process is
largely independent of the reaction mechanism (central versus peripheral
collisions, symmetric versus asymmetric systems, light ions versus heavy ion
induced reactions). Configurational energy fluctuations, that may give
important information on the heat capacity of the fragmenting system at the
freeze out stage, are not fully compatible among different data sets and
require further analysis to properly account for Coulomb effects and secondary
decays. Some basic theoretical questions, concerning the interplay between the
dynamics of the collision and the fragmentation process, and the cluster
definition in dense and hot media, are still open and are addressed at the end
of the paper. A comparison with realistic models and/or a quantitative analysis
of the fluctuation properties will be needed to clarify in the next future the
nature of the transition observed from compound nucleus evaporation to
multi-fragment production.Comment: Contribution to WCI (World Consensus Initiative) Book " "Dynamics and
Thermodynamics with Nuclear Degrees of Freedom", to appear on Euorpean
Physics Journal A as part of the Topical Volume. 9 pages, 12 figure
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