# pcSteiner

The Steiner tree problem is a well-known combinatorial optimization problem which asks a minimum spanning subtree containing a given subset of vertices (terminals). However, in many practical applications nodes and edges have an additional numerical value which represents their significance. That is where the Prize-Collecting Steiner Tree problem arises: the goal is to find a subgraph connecting all the terminals with the most expensive nodes and least expensive edges. Since this problem is proven to be NP-hard, exact and efficient algorithm does not exist. Loopy belief propagation can be utilised to obtain an approximate solution to this problem [1,2].

## Installation

To get the latest version of the package and install it from CRAN run the following command:

`install.packages("pcSteiner")`

## References

- M. Bayati, C. Borgs, A. Braunstein, J. Chayes, A. Ramezanpour, and R. Zecchina, “Statistical Mechanics of Steiner Trees”. PRL, 2008.
- I. Biazzo, A. Braunstein and R. Zecchina, “Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs”. PRL, 2012.