Answer Set Solving with Bounded Treewidth Revisited

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two kinds of graph representations of programs to exploit their treewidth as a parameter. Treewidth roughly measures to which extent the internal structure of a program resembles a tree. Our main contribution is the design of parameterized dynamic programming algorithms, which run in linear time if the treewidth and weights of the given program are bounded. Compared to previous work, our algorithms handle the full syntax of ASP. Finally, we report on an empirical evaluation that shows good runtime behaviour for benchmark instances of low treewidth, especially for counting answer sets.Comment: This paper extends and updates a paper that has been presented on the workshop TAASP'16 (arXiv:1612.07601). We provide a higher detail level, full proofs and more example

Assigning channels via the meet-in-the-middle approach

We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the $\ell$-bounded Channel Assignment (when the edge weights are bounded by $\ell$) running in time $O^*((2\sqrt{\ell+1})^n)$. This is the first algorithm which breaks the $(O(\ell))^n$ barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor. A major open problem asks whether Channel Assignment admits a $O(c^n)$-time algorithm, for a constant $c$ independent of $\ell$. We consider a similar question for Generalized T-Coloring, a CSP problem that generalizes \CA. We show that Generalized T-Coloring does not admit a $2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$-time algorithm, where $r$ is the size of the instance.Comment: SWAT 2014: 282-29

Cyanoresin, cyanoresin/cellulose triacetate blends for thin film, dielectric capacitors

Non brittle dielectric films are formed by blending a cyanoresin such as cyanoethyl, hydroxyethyl cellulose (CRE) with a compatible, more crystalline resin such as cellulose triacetate. The electrical breakdown strength of the blend is increased by orienting the films by uniaxial or biaxial stretching. Blends of high molecular weight CRE with high molecular weight cyanoethyl cellulose (CRC) provide films with high dielectric constants

Ionic modeling of lithium manganese spinel materials for use in rechargeable batteries

In order to understand and evaluate materials for use in Li ion rechargeable battery electrodes, we have modeled the crystal structures of various Mn oxide and Li Mn oxide compounds. We have modeled the MnO{sub 2} polymorphs and several spinels with intermediate compositions based on the amount of Li inserted into the tetrahedral site. 3-D representations of the structures provide a basis for identifying site occupancies, coordinations, Mn valence, order-disorder, and potentially new dopants for enhanced cathode behavior. XRD simulations of the crystal structures provide good agreement with observed patterns for synthesized samples. Ionic modeling of these materials consists of an energy minimization approach using Coulombic, repulsive, and van der Waals interactions. Modeling using electronic polarizabilities (shell model) allows a systematic analysis of changes in lattice energy, cell volume, and the relative stability of doped structures using ions such as Al, Ti, Ni, and Co

The Minimum Shared Edges Problem on Grid-like Graphs

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number $p$ of paths. On the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number $p$ of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter $k$, $p$, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure

Molecular modeling of the structure and dynamics of the interlayer and surface species of mixed-metal layered hydroxides: Chloride and water in hydrocalumite (Friedel’s salt)

The dynamical behavior of Cl{sup {minus}} and H{sub 2}O molecules in the interlayer and on the (001) surface of the Ca-aluminate hydrate hydrocalumite (Friedel's salt) over a range of temperatures from {minus}100 to 300 C is studied using the technique of isothermal-isobaric molecular dynamics computer simulations. This phase is currently the best available model compound for other, typically more disordered, mixed-metal layered hydroxides. The computed crystallographic parameters and density are in good agreement with available X-ray diffraction data and the force field developed for these simulations preserves the structure and density to within less than 2% of their measured values. In contrast to the highly ordered arrangement of the interlayer water molecules interpreted from the X-ray data, the simulations reveal significant dynamic disorder in water orientations. At all simulated temperatures, the interlayer water molecules undergo rapid librations (hindered hopping rotations) around an axis essentially perpendicular to the layers. This results in breaking and reformation of hydrogen bonds with the neighboring Cl{sup {minus}} anions and in a time-averaged nearly uniaxial symmetry at Cl{sup {minus}}, in good agreement with recent {sup 35}Cl NMR measurements. Power spectra of translational, vibrational, and vibrational motions of interlayer and surface Cl{sup {minus}} and H{sub 2}O were calculated as Fourier transforms of the atomic velocity autocorrelation functions and compared with the corresponding spectra and dynamics for a bulk aqueous solution. The ordered interlayer space has significant effects on the motions. Strong electrostatic attraction between interlayer water molecules and Ca atoms in the principal layer makes the Ca{hor_ellipsis}OH{sub 2} bond direction the preferred axis for interlayer water librations. The calculated diffusion coefficient of Cl{sup {minus}} as an outer-sphere surface complex is almost three times that of inner-sphere Cl{sup {minus}}, but is still about an order of magnitude less than that of Cl{sup {minus}} in bulk aqueous solution at the same temperature

NMR spectroscopic investigations of surface and interlayer species on minerals, clays and other oxides

The behavior of chemical species adsorbed on solid surfaces and exchanged into clay interlayers plays a significant role in controlling many natural and technologically important processes, including rheological behavior, catalysis, plant growth, transport in natural pore fluids and those near anthropogenic hazardous waste sites, and water-mineral interaction. Adsorption and exchange reactions have been the focus of intense study for many decades. Only more recently, however, have there been extensive spectroscopic studies of surface species. Among the spectroscopic methods useful for studying surface and exchanged species (e.g., infrared, X-ray photoelectron spectroscopy [XPS] and X-ray absorption spectroscopy [XAS]), nuclear magnetic resonance spectroscopy (NMR) has the considerable advantage of providing not only structural information via the chemical shift and quadrupole coupling constant but dynamical information in the Hz-mHz range via lineshape analysis and relaxation rate measurements. It is also possible to obtain data in the presence of a separate fluid phase, which is essential for many applications. This paper illustrates the range of applications of NMR methods to surface and exchanged species through review of recent work from our laboratory on Cs in clay interlayers and Cs, Na and phosphate adsorbed on oxide surfaces. The substrate materials used for these experiments and our long-term objectives are related to problems of geochemical interest, but the principals and techniques are of fundamental interest and applicable to a wide range of technological problems

The Power of Cut-Based Parameters for Computing Edge Disjoint Paths

This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our aim is to identify structural properties (parameters) of graphs which allow the efficient solution of EDP without restricting the placement of terminals in P in any way. In this setting, EDP is known to remain NP-hard even on extremely restricted graph classes, such as graphs with a vertex cover of size 3. We present three results which use edge-separator based parameters to chart new islands of tractability in the complexity landscape of EDP. Our first and main result utilizes the fairly recent structural parameter treecut width (a parameter with fundamental ties to graph immersions and graph cuts): we obtain a polynomial-time algorithm for EDP on every graph class of bounded treecut width. Our second result shows that EDP parameterized by treecut width is unlikely to be fixed-parameter tractable. Our final, third result is a polynomial kernel for EDP parameterized by the size of a minimum feedback edge set in the graph