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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}}} .
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.
This set of choices corresponds to the following solution to the pentomino tiling problem: A pentomino tiling problem is more naturally viewed as an exact cover problem than an exact hitting set problem, because it is more natural to view each choice as a set of constraints than each constraint as a set of choices.
A combination of function coverage and branch coverage is sometimes also called decision coverage. This criterion requires that every point of entry and exit in the program has been invoked at least once, and every decision in the program has taken on all possible outcomes at least once.
When this algorithm terminates, either all inputs are in the subset (which is obviously optimal), or there is an input that does not fit. The first such input is smaller than all previous inputs that are in the subset and the sum of inputs in the subset is more than T/2 otherwise the input also is less than T/2 and it would fit in the set. Such ...
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element).
-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 ...
Set covering is equivalent to the hitting set problem. That is seen by observing that an instance of set covering can be viewed as an arbitrary bipartite graph, with the universe represented by vertices on the left, the sets represented by vertices on the right, and edges representing the membership of elements to sets. The task is then to find ...