Graph editing to a fixed target

For a fixed graph H, the H-Minor Edit problem takes as input a graph G and an integer k and asks whether G can be modified into H by a total of at most k edge contractions, edge deletions and vertex deletions. Replacing edge contractions by vertex dissolutions yields the H-Topological Minor Edit problem. For each problem we show polynomial-time solvable and NP-complete cases depending on the choice of H. Moreover, when G is AT-free, chordal or planar, we show that H-Minor Edit is polynomial-time solvable for all graphs H

L-Drawings of Directed Graphs

We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive $x$- and $y$-coordinates and edges consist of two segments, one exiting the source vertically and one entering the destination horizontally. We study the problem of computing L-drawings using minimum ink. We prove its NP-completeness and provide a heuristics based on a polynomial-time algorithm that adds a vertex to a drawing using the minimum additional ink. We performed an experimental analysis of the heuristics which confirms its effectiveness.Comment: 11 pages, 7 figure

All-Electrical Quantum Computation with Mobile Spin Qubits

We describe and discuss a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Static electric fields are used to implement a universal set of quantum gates, via the spin-orbit and exchange couplings. Initialization and measurement can be performed either by spin injection from/to ferromagnets, or by using spin filters and mesoscopic spin polarizing beam-splitters. The vulnerability of this proposal to various sources of error is estimated by numerical simulations. We also assess the suitability of various materials currently used in nanotechnology for an actual implementation of our model.Comment: 10 pages, 6 figs, RevTeX

Electron Spins in Artificial Atoms and Molecules for Quantum Computing

Achieving control over the electron spin in quantum dots (artificial atoms) or real atoms promises access to new technologies in conventional and in quantum information processing. Here we review our proposal for quantum computing with spins of electrons confined to quantum dots. We discuss the basic requirements for implementing spin-qubits, and describe a complete set of quantum gates for single- and two-qubit operations. We show how a quantum dot attached to leads can be used for spin filtering and spin read-out, and as a spin-memory device. Finally, we focus on the experimental characterization of the quantum dot systems, and discuss transport properties of a double-dot and show how Kondo correlations can be used to measure the Heisenberg exchange interaction between the spins of two dots.Comment: 13 pages, 8 figures, Invited Review (Semiconductor Spintronics, Special Issue of SST

The readout of the fullerene-based quantum computing by a scanning tunneling microscope

We consider to detect the electron spin of a doped atom, i.e., a nitrogen or a phosphorus, caged in a fullerene by currently available technique of the scanning tunneling microscope (STM), which actually corresponds to the readout of a qubit in the fullerene-based quantum computing. Under the conditions of polarized STM current and Coulomb blockade, we investigate the tunneling matrix elements involving the exchange coupling between the tunneling polarized electrons and the encapsulated polarized electron, and calculate the variation of the tunneling current with respect to different orientations of the encapsulated electron spin. The experimental feasibility of our scheme is discussed under the consideration of some imperfect factors.Comment: RevTex file, 3 figures. To appear in New Journal of Physic

Bezpieczeństwo i ryzyko podróżowania tanimi liniami lotniczymi

Golovach, E. P.; Rubahov, A. I. Safety and risks of traveling with low-cost airlinesDecydując się na podróż samolotem, jednym z najważniejszych czynników jakie potencjalny turysta bieżę pod uwagę jest kwestia bezpieczeństwa. Szczególnego znaczenia ten czynnik nabiera zwłaszcza w dobie nagłaśnianych i szeroko omawianych katastrof lotniczych w różnych częściach świata oraz bankructwie tanich linii lotniczych w ostatnich latach. W referacie zostali omówione czynniki mające wpływ na bezpieczeństwo i ryzyko podróżowania tanimi liniami lotniczymi. Przedstawione obszary z największą liczbą ofiar wypadków cyvilnych statków powietrznych

Line-distortion, Bandwidth and Path-length of a graph

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph $G$ can be embedded into the line with distortion $k$, then $G$ admits a Robertson-Seymour's path-decomposition with bags of diameter at most $k$ in $G$; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem

Spin relaxation at the singlet-triplet crossing in a quantum dot

We study spin relaxation in a two-electron quantum dot in the vicinity of the singlet-triplet crossing. The spin relaxation occurs due to a combined effect of the spin-orbit, Zeeman, and electron-phonon interactions. The singlet-triplet relaxation rates exhibit strong variations as a function of the singlet-triplet splitting. We show that the Coulomb interaction between the electrons has two competing effects on the singlet-triplet spin relaxation. One effect is to enhance the relative strength of spin-orbit coupling in the quantum dot, resulting in larger spin-orbit splittings and thus in a stronger coupling of spin to charge. The other effect is to make the charge density profiles of the singlet and triplet look similar to each other, thus diminishing the ability of charge environments to discriminate between singlet and triplet states. We thus find essentially different channels of singlet-triplet relaxation for the case of strong and weak Coulomb interaction. Finally, for the linear in momentum Dresselhaus and Rashba spin-orbit interactions, we calculate the singlet-triplet relaxation rates to leading order in the spin-orbit interaction, and find that they are proportional to the second power of the Zeeman energy, in agreement with recent experiments on triplet-to-singlet relaxation in quantum dots.Comment: 29 pages, 14 figures, 1 tabl

On retracts, absolute retracts, and folds in cographs

Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the size of H. When restricted to the class of threshold graphs or to the class of trivially perfect graphs, the problem becomes tractable in polynomial time. The problem is also soluble when one cograph is given as an induced subgraph of the other. We characterize absolute retracts of cographs.Comment: 15 page