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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}}} .
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 ...
For example, the constraint set for column 1 and number 1, which can be labeled C1#1, contains the 9 possibilities for column 1 and number 1 but different rows: C1#1 = { R1C1#1, R2C1#1, R3C1#1, R4C1#1, R5C1#1, R6C1#1, R7C1#1, R8C1#1, R9C1#1 }. Box-Number: A box-number constraint set contains all the possibilities for a particular box and number ...
In the fractional set cover problem, it is allowed to select fractions of sets, rather than entire sets. A fractional set cover is an assignment of a fraction (a number in [0,1]) to each set in , such that for each element x in the universe, the sum of fractions of sets that contain x is at least 1. The goal is to find a fractional set cover in ...
-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 ...
In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original. Common examples of array slicing are extracting a substring from a string of characters, the " ell " in "h ell o", extracting a row or column from a two ...
Graphillion, A Python-based graphset manipulation library based on SAPPOROBDD, developed and maintained by Minato's research group that is heavily focused on ZDD-based algorithms. The library consists of an optimized C/C++ core and a python interface. TdZdd: A header-only C++ library for BDD/ZDD manipulation. pyzdd: A python wrapper over TdZdd.
The covering number quantifies the size of a set and can be applied to general metric spaces. Two related concepts are the packing number, the number of disjoint balls that fit in a space, and the metric entropy, the number of points that fit in a space when constrained to lie at some fixed minimum distance apart.