https://github.com/euxhenh/multiset-multicover

Multiset multicover using the extended greedy cover algorithm implemented in C++ and exposed to Python.
https://github.com/euxhenh/multiset-multicover

cover cpp multiset python set set-cover set-cover-problem

Last synced: about 4 hours ago
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Multiset multicover using the extended greedy cover algorithm implemented in C++ and exposed to Python.

• Host: GitHub
• URL: https://github.com/euxhenh/multiset-multicover
• Owner: euxhenh
• License: mit
• Created: 2021-12-22T11:49:04.000Z (over 4 years ago)
• Default Branch: main
• Last Pushed: 2022-10-07T19:57:12.000Z (over 3 years ago)
• Last Synced: 2025-02-16T09:39:06.462Z (about 1 year ago)
• Topics: cover, cpp, multiset, python, set, set-cover, set-cover-problem
• Language: C++
• Homepage:
• Size: 67.4 KB
• Stars: 5
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.rst
  • License: LICENSE

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README

          
.. role:: python(code)

   :language: python

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 :python:`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

.. code:: bash

    $ pip install multiset-multicover