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