An efficient algorithm listing all minimal vertex separators of an undirected graph is given. The algorithm needs polynomial time per separator that is found.

In this paper we give an efficient algorithm to find all minimal vertex separators of an undirected graph. The algorithm needs polynomial time per separat.or that. is found.

We present an efficient algorithm that lists the minimal separators of a 3-connected planar graph in O(n) per separator.

We consider the largest number of minimal separators a graph on n vertices can have at most. – We give a new proof that this number is in O ((

Graph separation is a well-known tool to make (hard) graph problems accessible to a divide-and-conquer approach. We show how to use graph separator theorems in combination with (linear) problem kernels in order to develop fixed parameter algorithms for many wellknown NP-hard (planar) graph problems. We coin the key notion of glueable select&verify graph problems and derive from that a prospecti...

We focus on binary classification problems; that is, we consider the problem of predicting a binary label y based on its corresponding input vector x. As in the standard machine learning formulation, we assume that the data points (x, y) are drawn from an unknown underlying distribution DXY over X × Y ; X is called the instance space and Y is the label space. We assume that Y = {±1} and X = Rd;...

For a connected graph G = (V,E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U)∪{u} is connected. In that case U is called a minimal disconnected cut. We show that the problem of testing whether a graph has a minimal disconnected cut i...

In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \ {P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ...

Development of hydrocyclonic separation is introduced first. The characteristics of the dynamic hydrocyclone are described. The laboratory study and oilfield tests of dynamic hydrocyclones were carried out. Some photos indicating flow phenomena inside the hydrocyclone were taken and analyzed for understanding the effect of some varieties on hydrocyclonic separation. Relations of flowrate, and o...