498 research outputs found

### Explaining Snapshots of Network Diffusions: Structural and Hardness Results

Much research has been done on studying the diffusion of ideas or
technologies on social networks including the \textit{Influence Maximization}
problem and many of its variations. Here, we investigate a type of inverse
problem. Given a snapshot of the diffusion process, we seek to understand if
the snapshot is feasible for a given dynamic, i.e., whether there is a limited
number of nodes whose initial adoption can result in the snapshot in finite
time. While similar questions have been considered for epidemic dynamics, here,
we consider this problem for variations of the deterministic Linear Threshold
Model, which is more appropriate for modeling strategic agents. Specifically,
we consider both sequential and simultaneous dynamics when deactivations are
allowed and when they are not. Even though we show hardness results for all
variations we consider, we show that the case of sequential dynamics with
deactivations allowed is significantly harder than all others. In contrast,
sequential dynamics make the problem trivial on cliques even though it's
complexity for simultaneous dynamics is unknown. We complement our hardness
results with structural insights that can help better understand diffusions of
social networks under various dynamics.Comment: 14 pages, 3 figure

### Upper and Lower Bounds for Weak Backdoor Set Detection

We obtain upper and lower bounds for running times of exponential time
algorithms for the detection of weak backdoor sets of 3CNF formulas,
considering various base classes. These results include (omitting polynomial
factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set
of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm
to detect whether there is a weak backdoor set of at most k variables into the
class of Krom formulas. These bounds improve an earlier known bound of 6^k. We
also prove a 2^k lower bound for these problems, subject to the Strong
Exponential Time Hypothesis.Comment: A short version will appear in the proceedings of the 16th
International Conference on Theory and Applications of Satisfiability Testin

### Using contracted solution graphs for solving reconfiguration problems.

We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs

### Surjective H-Colouring over reflexive digraphs

The Surjective H-Colouring problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce endo-triviality, the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theoretic classifications of Surjective H-Colouring in the case of reflexive digraphs. Chen (2014) proved, in the setting of constraint satisfaction problems, that Surjective H-Colouring is NP-complete if H has the property that all of its polymorphisms are essentially unary. We give the first concrete application of his result by showing that every endo-trivial reflexive digraph H has this property. We then use the concept of endo-triviality to prove, as our main result, a dichotomy for Surjective H-Colouring when H is a reflexive tournament: if H is transitive, then Surjective H-Colouring is in NL; otherwise, it is NP-complete. By combining this result with some known and new results, we obtain a complexity classification for Surjective H-Colouring when H is a partially reflexive digraph of size at most 3

### Using contracted solution graphs for solving reconfiguration problems

We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs

### Deeply virtual Compton scattering in next-to-leading order

We study the amplitude of deeply virtual Compton scattering in
next-to-leading order of perturbation theory including the two-loop evolution
effects for different sets of skewed parton distributions (SPDs). It turns out
that in the minimal subtraction scheme the relative radiative corrections are
of order 20-50%. We analyze the dependence of our predictions on the choice of
SPD, that will allow to discriminate between possible models of SPDs from
future high precision experimental data, and discuss shortly theoretical
uncertainties induced by the radiative corrections.Comment: 10 pages, LaTeX, 3 figure

### Radiative corrections to deeply virtual Compton scattering

We discuss possibilities of measurement of deeply virtual Compton scattering
amplitudes via different asymmetries in order to access the underlying skewed
parton distributions. Perturbative one-loop coefficient functions and two-loop
evolution kernels, calculated recently by a tentative use of residual conformal
symmetry of QCD, are used for a model dependent numerical estimation of
scattering amplitudes.Comment: 9 pages LaTeX, 3 figures, czjphyse.cls required Talk given by D.
M\"uller at Inter. Workshop ``PRAHA-Spin99'', Prague, Sept. 6-11, 199

### Surface roughness during depositional growth and sublimation of ice crystals

Full version of an earlier discussion paper (Chou et al. 2018)Ice surface properties can modify the scattering properties of atmospheric ice crystals and therefore affect the radiative properties of mixed-phase and cirrus clouds. The Ice Roughness Investigation System (IRIS) is a new laboratory setup designed to investigate the conditions under which roughness develops on single ice crystals, based on their size, morphology and growth conditions (relative humidity and temperature). Ice roughness is quantified through the analysis of speckle in 2-D light-scattering patterns. Characterization of the setup shows that a supersaturation of 20 % with respect to ice and a temperature at the sample position as low as-40 Â°C could be achieved within IRIS. Investigations of the influence of humidity show that higher supersaturations with respect to ice lead to enhanced roughness and irregularities of ice crystal surfaces. Moreover, relative humidity oscillations lead to gradual ratcheting-up of roughness and irregularities, as the crystals undergo repeated growth-sublimation cycles. This memory effect also appears to result in reduced growth rates in later cycles. Thus, growth history, as well as supersaturation and temperature, influences ice crystal growth and properties, and future atmospheric models may benefit from its inclusion in the cloud evolution process and allow more accurate representation of not just roughness but crystal size too, and possibly also electrification properties.Peer reviewe

### Augmenting graphs to minimize the diameter

We study the problem of augmenting a weighted graph by inserting edges of
bounded total cost while minimizing the diameter of the augmented graph. Our
main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure

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