This package implements the Greedy Cover algorithm for multisets in C++ and exposes it to Python. Given a universe of elements U, and a family of subsets F = {S1, ..., Sn} of U, the set cover problem asks to find the smallest number of sets in F such that every element of U appears in at least one such set. This can be extended to a multicover problem, where we ask that every element be included at least k sets. This in turn, can be extended to accomodate multisets, where each element in Si also has a given multiplicity.

The set cover problem is NP hard. The best known algorithm is a greedy approach that iteratively selects the set with the largest number of elements that have not been covered yet. This algorithm has a log(n)-approximation guarantee where n is the size of the largest set. The same guarantee also applies to the multicover problem, as well as the multiset multicover problem (n here corresponds to the size of the largest set, counting multiplicities).

Basic Example

To run the greedy cover algorithm, one needs to create a GreedyCoverInstance object and add multisets to it. The coverage factor can be a single integer or a specific integer for each element in U. The solution is a list of integers corresponding to the index of the sets included (in order of selection).

NOTE: Make sure any numpy arrays are converted to lists by calling arr.tolist().

>>> import multiset_multicover as mm

>>> gci = mm.GreedyCoverInstance(4)
>>> gci.add_multiset([1, 2, 3])  # if no multiplicity provided, it defaults to 1
>>> gci.add_multiset([0, 1, 2], multiplicity=[2, 3, 1])
>>> gci.add_multiset([0, 1, 2, 3])

>>> gci.cover(1)
Output: [2]
>>> gci.cover([2, 1, 1, 1])
Output: [1, 0]

For more detailed explanation see doc.

Installation

To install this package, run

$ pip install multiset-multicover