Dynamic Programming: The Next Step

Since 2013, dynamic programming (DP)-based plan generators are capable of correctly reordering not only inner joins, but also outer joins. Now, we consider the next big step: reordering not only joins, but also joins and grouping. Since only reorderings of grouping with inner joins are known, we first develop equivalences which allow reordering of grouping with outer joins. Then, we show how to extend a state-of-the-art DP-based plan generator to fully explore these new plan alternatives

Extending dynamic-programming-based plan generators: beyond pure enumeration

The query optimizer plays an important role in a database management system supporting a declarative query language, such as SQL. One of its central components is the plan generator, which is responsible for determining the optimal join order of a query. Plan generators based on dynamic programming have been known for several decades. However, some significant progress in this field has only been made recently. This includes the emergence of highly efficient enumeration algorithms and the ability to optimize a wide range of queries by supporting complex join predicates. This thesis builds upon the recent advancements by providing a framework for extending the aforementioned algorithms. To this end, a modular design is proposed that allows for the exchange of individual parts of the plan generator, thus enabling the implementor to add new features at will. This is demonstrated by taking the example of two previously unsolved problems, namely the correct and complete reordering of different types of join operators as well as the efficient reordering of join operators and grouping operators

Edge channel confinement in a bilayer graphene nn-pp-nn quantum dot

We combine electrostatic and magnetic confinement to define a quantum dot in bilayer graphene. The employed geometry couples $n$-doped reservoirs to a $p$-doped dot. At magnetic field values around $B = 2~$T, Coulomb blockade is observed. This demonstrates that the coupling of the co-propagating modes at the $p$-$n$ interface is weak enough to form a tunnel barrier, facilitating transport of single charge carriers onto the dot. This result may be of use for quantum Hall interferometry experiments

Interactions and magnetotransport through spin-valley coupled Landau levels in monolayer MoS2_{2}

The strong spin-orbit coupling and the broken inversion symmetry in monolayer transition metal dichalcogenides (TMDs) results in spin-valley coupled band structures. Such a band structure leads to novel applications in the fields of electronics and optoelectronics. Density functional theory calculations as well as optical experiments have focused on spin-valley coupling in the valence band. Here we present magnetotransport experiments on high-quality n-type monolayer molybdenum disulphide (MoS$_{2}$) samples, displaying highly resolved Shubnikov-de Haas oscillations at magnetic fields as low as $2~T$. We find the effective mass $0.7~m_{e}$, about twice as large as theoretically predicted and almost independent of magnetic field and carrier density. We further detect the occupation of the second spin-orbit split band at an energy of about $15~meV$, i.e. about a factor $5$ larger than predicted. In addition, we demonstrate an intricate Landau level spectrum arising from a complex interplay between a density-dependent Zeeman splitting and spin and valley-split Landau levels. These observations, enabled by the high electronic quality of our samples, testify to the importance of interaction effects in the conduction band of monolayer MoS$_{2}$.Comment: Phys.Rev.Lett. (2018

Shell Filling and Trigonal Warping in Graphene Quantum Dots

Transport measurements through a few-electron circular quantum dot in bilayer graphene display bunching of the conductance resonances in groups of four, eight and twelve. This is in accordance with the spin and valley degeneracies in bilayer graphene and an additional threefold 'minivalley degeneracy' caused by trigonal warping. For small electron numbers, implying a small dot size and a small displacement field, a two-dimensional s- and then a p-shell are successively filled with four and eight electrons, respectively. For electron numbers larger than twelve, as the dot size and the displacement field increase, the single-particle ground state evolves into a three-fold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.Comment: 10 pages, 7 figure

Spin and Valley States in Gate-defined Bilayer Graphene Quantum Dots

In bilayer graphene, electrostatic confinement can be realized by a suitable design of top and back gate electrodes. We measure electronic transport through a bilayer graphene quantum dot, which is laterally confined by gapped regions and connected to the leads via p-n junctions. Single electron and hole occupancy is realized and charge carriers $n = 1, 2,\dots 50$ can be filled successively into the quantum system with charging energies exceeding $10 \ \mathrm{meV}$. For the lowest quantum states, we can clearly observe valley and Zeeman splittings with a spin g-factor of$g_{s}\approx 2$. In the low field-limit, the valley splitting depends linearly on the perpendicular magnetic field and is in qualitative agreement with calculations.Comment: 7 pages, 4 figure