Computing graph separators is an important step in many graph algorithms. A popular technique for finding separators involves spectral methods. However, there has not been much prior analysis of the quality of the separators produced by this technique; instead it is usually claimed that spectral methods “work well in practice.” We present an initial attempt at such analysis. In particular, we c...

The following algorithm partitions road networks surprisingly well: (i) sort the vertices by longitude (or latitude, or some linear combination) and (ii) compute the maximum flow from the first k nodes (forming the source) to the last k nodes (forming the sink). Return the corresponding minimum cut as an edge separator (or recurse until the resulting subgraphs are sufficiently small).

Separators present the crucial functions of separating positive and negative electrodes due to free flow lithium ions through liquid electrolyte that fills in their open pore. for Lithium-ion batteries can be classified into porous polymeric membranes, nonwoven mats, cellulose separators. When a lithium-ion battery is being overcharged, it releases heat results inner-short. The polyethylene (PE...