406 research outputs found
Why Is Dual-Pivot Quicksort Fast?
I discuss the new dual-pivot Quicksort that is nowadays used to sort arrays
of primitive types in Java. I sketch theoretical analyses of this algorithm
that offer a possible, and in my opinion plausible, explanation why (a)
dual-pivot Quicksort is faster than the previously used (classic) Quicksort and
(b) why this improvement was not already found much earlier.Comment: extended abstract for Theorietage 2015
(https://www.uni-trier.de/index.php?id=55089) (v2 fixes a small bug in the
pseudocode
Efficient Algorithms for Envy-Free Stick Division With Fewest Cuts
Given a set of n sticks of various (not necessarily different) lengths, what
is the largest length so that we can cut k equally long pieces of this length
from the given set of sticks? We analyze the structure of this problem and show
that it essentially reduces to a single call of a selection algorithm; we thus
obtain an optimal linear-time algorithm.
This algorithm also solves the related envy-free stick-division problem,
which Segal-Halevi, Hassidim, and Aumann (AAMAS, 2015) recently used as their
central primitive operation for the first discrete and bounded envy-free cake
cutting protocol with a proportionality guarantee when pieces can be put to
waste.Comment: v3 adds more context about the proble
Exploring light mediators with low-threshold direct detection experiments
We explore the potential of future cryogenic direct detection experiments to
determine the properties of the mediator that communicates the interactions
between dark matter and nuclei. Due to their low thresholds and large
exposures, experiments like CRESST-III, SuperCDMS SNOLAB and EDELWEISS-III will
have excellent capability to reconstruct mediator masses in the MeV range for a
large class of models. Combining the information from several experiments
further improves the parameter reconstruction, even when taking into account
additional nuisance parameters related to background uncertainties and the dark
matter velocity distribution. These observations may offer the intriguing
possibility of studying dark matter self-interactions with direct detection
experiments.Comment: 19 pages, 10 figures + appendices. Matches published versio
Self-interacting dark matter with a stable vector mediator
Light vector mediators can naturally induce velocity-dependent dark matter
self-interactions while at the same time allowing for the correct dark matter
relic abundance via thermal freeze-out. If these mediators subsequently decay
into Standard Model states such as electrons or photons however, this is
robustly excluded by constraints from the Cosmic Microwave Background. We study
to what extent this conclusion can be circumvented if the vector mediator is
stable and hence contributes to the dark matter density while annihilating into
lighter degrees of freedom. We find viable parts of parameter space which lead
to the desired self-interaction cross section of dark matter to address the
small-scale problems of the collisionless cold dark matter paradigm while being
compatible with bounds from the Cosmic Microwave Background and Big Bang
Nucleosynthesis observations.Comment: 25 pages, 6 figures. Matches published versio
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