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A subset Q of J is called a rainbow set if it contains at most a single interval of each color. A set of intervals J is called a covering of P if each point in P is contained in at least one interval of Q. The Rainbow covering problem is the problem of finding a rainbow set Q that is a covering of P. The problem is NP-hard (by reduction from ...
The greedy algorithm for maximum coverage chooses sets according to one rule: at each stage, choose a set which contains the largest number of uncovered elements. It can be shown that this algorithm achieves an approximation ratio of 1 − 1 e {\displaystyle 1-{\frac {1}{e}}} .
Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of the best solution from some set of available alternatives, [1] by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process.
Another variant of bin packing of interest in practice is the so-called online bin packing. Here the items of different volume are supposed to arrive sequentially, and the decision maker has to decide whether to select and pack the currently observed item, or else to let it pass. Each decision is without recall.
Geometric set cover is a special case of Set Cover when the universe is a set of points in and the sets are induced by the intersection of the universe and geometric shapes (e.g., disks, rectangles). Set packing; Maximum coverage problem is to choose at most k sets to cover as many elements as possible.
In the mathematical field of combinatorics, given a collection of subsets of a set, an exact cover is a subcollection of such that each element in is contained in exactly one subset in . One says that each element in X {\displaystyle X} is covered by exactly one subset in S ∗ {\displaystyle {\mathcal {S}}^{*}} . [ 1 ]
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
-l (--long-file-names): Create long file names for included source files. For example, if the header file x.h contains code, and was included in the file a.c, then running gcov on the file a.c will produce an output file called a.c##x.h.gcov instead of x.h.gcov. This can be useful if x.h is included in multiple source files and you want to see ...