DeepAI AI Chat
Log In Sign Up

A Linear Programming Based Approach to the Steiner Tree Problem with a Fixed Number of Terminals

by   Matias Siebert, et al.

We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our main result is that the linear programming (LP) relaxation of each IP is integral so that it can be solved as a linear program. However, the number of IPs grows exponentially with the number of terminals in the Steiner tree. As a consequence, we are able to solve the Steiner tree problem by solving a polynomial number of LPs, when the number of terminals is fixed.


page 1

page 2

page 3

page 4


A Simulated Annealing Algorithm for the Directed Steiner Tree Problem

In <cit.> the authors present a set of integer programs (IPs) for the St...

A scaleable projection-based branch-and-cut algorithm for the p-center problem

The p-center problem (pCP) is a fundamental problem in location science,...

Fractional Decomposition Tree Algorithm: A tool for studying the integrality gap of Integer Programs

We present a new algorithm, Fractional Decomposition Tree (FDT) for find...

Consistency for 0-1 Programming

Concepts of consistency have long played a key role in constraint progra...

Advances in Bayesian Network Learning using Integer Programming

We consider the problem of learning Bayesian networks (BNs) from complet...

Load Disaggregation Based on Aided Linear Integer Programming

Load disaggregation based on aided linear integer programming (ALIP) is ...

Adaptive Partition-based SDDP Algorithms for Multistage Stochastic Linear Programming

In this paper, we extend the adaptive partition-based approach for solvi...