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In computational complexity theory, the set splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S 1, S 2 such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S 1 or S 2.
Product partition is the problem of partitioning a set of integers into two sets with the same product (rather than the same sum). This problem is strongly NP-hard. [14] Kovalyov and Pesch [15] discuss a generic approach to proving NP-hardness of partition-type problems.
A split graph may have more than one partition into a clique and an independent set; for instance, the path a–b–c is a split graph, the vertices of which can be partitioned in three different ways: the clique {a, b} and the independent set {c} the clique {b, c} and the independent set {a} the clique {b} and the independent set {a, c}
A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...
Therefore, the remaining 3-sets can be partitioned into two groups: n 3-sets containing the items u ij, and n 3-sets containing the items u ij '. In each matching pair of 3-sets, the sum of the two pairing items u ij +u ij ' is 44T+4, so the sum of the four regular items is 84T+4. Therefore, from the four regular items, we construct a 4-set in ...
Since every partition of the samples into two sets is separable by a linear separator, the property follows. The left image shows 100 points in the two dimensional real space, labelled according to whether they are inside or outside the circular area.
A point in the intersection of these convex hulls is called a Radon point of the set. Two sets of four points in the plane (the vertices of a square and an equilateral triangle with its centroid), the multipliers solving the system of three linear equations for these points, and the Radon partitions formed by separating the points with positive ...
H 1 does not separate the sets. H 2 does, but only with a small margin. H 3 separates them with the maximum margin. Classifying data is a common task in machine learning. Suppose some data points, each belonging to one of two sets, are given and we wish to create a model that will decide which set a new data point will be in.