International audienceWe propose a new algorithm for the classical problem of computing the diameter of undirected unweighted graphs, namely, the maximum distance among all the pairs of nodes, where the distance of a pair of nodes is the number of edges contained in the shortest path connecting these two nodes. Although its worst-case complexity is O(nm) time, where n is the number of nodes and m is the number of edges of the graph, we experimentally show that our algorithm works in O(m) time in practice, requiring few breadth-first searches to complete its task on almost 200 real-world graphs

The addition of [2.2.2]cryptand (C222) to sodium dodecyl sulfate (SDS) micelles in aqueous solution is studied by small-angle neutron scattering (SANS). Hydrogenated and perdeuterated SDS micelles with 8% (wt/wt) concentration have been studied in the presence of 0.5, 1.0, and 1.5 mole ratio C222/surfactant. SANS analysis was performed using a two-shell model for the micelle form factor (core plus interfacial layer) and a screened Coulomb interactive potential for the interparticles potential. For both deuterated and hydrogenated surfactant, C222 ligand complexes the sodium micellar counterion and is mainly located at the interface partially screening the micelle surface charge. Counterion complexation produces, as compared to pure SDS micellar solutions, an increase of the interfacial layer thickness and a decrease of the micellar surface charge, of the contact potential, and of the average aggregation number. We report a detailed analysis of the micelle structure and intermicellar interaction potential.

Aqueous sodium dodecyl sulfate micellar solutions were investigated by a recently developed doubledifferential dielectric spectroscopy technique in the frequency range 100 MHz-3 GHz at 22 • C, in the surfactant concentration range 29.8-524 mM, explored for the first time above 104 mM. The micellar contribution to dielectric spectra was analyzed according to three models containing, respectively, a single Debye relaxation, a Cole-Cole relaxation and a double Debye relaxation. The single Debye model is not accurate enough. Both Cole-Cole and double Debye models fit well the experimental dielectric spectra. With the double Debye model, two characteristic relaxation times were identified: the slower one, in the range 400-900 ps, is due to the motion of counterions bound to the micellar surface (lateral motion); the faster one, in the range 100-130 ps, is due to interfacial bound water. Time constants and amplitudes of both processes are in fair agreement with Grosse's theoretical model, except at the largest concentration values, where interactions between micelles increase. For each sample, the volume fraction of bulk water and the effect of bound water as well as the conductivity in the low frequency limit were computed. The bound water increases as the surfactant concentration increases, in quantitative agreement with the micellar properties. The number of water molecules per surfactant molecule was also computed. The conductivity values are in agreement with Kallay's model over the whole surfactant concentration range.

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