Advanced Multilevel Node Separator Algorithms

A node separator of a graph is a subset S of the nodes such that removing S and its incident edges divides the graph into two disconnected components of about equal size. In this work, we introduce novel algorithms to find small node separators in large graphs. With focus on solution quality, we introduce novel flow-based local search algorithms which are integrated in a multilevel framework. In addition, we transfer techniques successfully used in the graph partitioning field. This includes the usage of edge ratings tailored to our problem to guide the graph coarsening algorithm as well as highly localized local search and iterated multilevel cycles to improve solution quality even further. Experiments indicate that flow-based local search algorithms on its own in a multilevel framework are already highly competitive in terms of separator quality. Adding additional local search algorithms further improves solution quality. Our strongest configuration almost always outperforms competing systems while on average computing 10% and 62% smaller separators than Metis and Scotch, respectively

Fractionation of cellulose nanocrystals : enhancing liquid crystal ordering without promoting gelation

Colloids of electrically charged nanorods can spontaneously develop a fluid yet ordered liquid crystal phase, but this ordering competes with a tendency to form a gel of percolating rods. The threshold for ordering is reduced by increasing the rod aspect ratio, but the percolation threshold is also reduced with this change; hence, prediction of the outcome is nontrivial. Here, we show that by establishing the phase behavior of suspensions of cellulose nanocrystals (CNCs) fractionated according to length, an increased aspect ratio can strongly favor liquid crystallinity without necessarily influencing gelation. Gelation is instead triggered by increasing the counterion concentration until the CNCs lose colloidal stability, triggering linear aggregation, which promotes percolation regardless of the original rod aspect ratio. Our results shine new light on the competition between liquid crystal formation and gelation in nanoparticle suspensions and provide a path for enhanced control of CNC self-organization for applications in photonic crystal paper or advanced composites