# Interval Spanning Trees Problem: Solvability and Computational Complexity

@inproceedings{Kozina1994IntervalST, title={Interval Spanning Trees Problem: Solvability and Computational Complexity}, author={Galina Kozina and Vitaly A. Perepelitsa}, year={1994} }

The optimization Spanning Trees Problem on graphs with interval weights is presented. The interval function is defined as the sum of interval weights of feasible spanning tree edges. The relation order introduced into set of feasible solutions generates the Pareto set which is considered as the solution of the interval problem. The questions of solvability and computational complexity are investigated by applying the multicriterial approach.

## 24 Citations

On the complexity of the robust spanning tree problem with interval data

- Mathematics, Computer ScienceOper. Res. Lett.
- 2004

A Constraint Satisfaction Approach to the Robust Spanning Tree Problem with Interval Data

- Computer Science, MathematicsUAI
- 2002

This paper considers the robust spanning tree problem with interval data and proposes a constraint satisfaction approach using a combinatorial lower bound, a pruning component that removes infeasible and suboptimal edges, as well as a search strategy exploring the most uncertain edges first.

A Benders decomposition approach for the robust spanning tree problem with interval data

- Computer ScienceEur. J. Oper. Res.
- 2006

Interval-parameter optimization problems on graphs

- Mathematics, Computer Science
- 2009

Well-known optimization problems on graphs are considered under uncertainty when parameter domains are specified in the form of intervals, and sufficient conditions of statistical efficiency of a proposed approximate algorithm are constructively substantiated.

How informative are Minimum Spanning Tree algorithms?

- Computer Science2014 IEEE International Symposium on Information Theory
- 2014

This paper investigates noisy versions of the Minimum Spanning Tree (MST) problem and compares the generalization properties of MST algorithms and provides insights for algorithm design when noise in combinatorial optimization is unavoidable.

Simulated annealing algorithm for the robust spanning tree problem

- Computer ScienceJ. Heuristics
- 2008

This is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem with interval data, namely simulated annealing, in order to calculate an approximate solution for large scale instances efficiently.

A branch and bound algorithm for the robust spanning tree problem with interval data

- Computer ScienceEur. J. Oper. Res.
- 2005

Heuristics for the central tree problem

- Business, Computer ScienceJ. Heuristics
- 2010

This paper addresses the central spanning tree problem with a hybrid heuristic consisting of: (1) a greedy construction heuristic to get a good initial solution and (2) fast local search improvement.

Constructor design problem under uncertain data

- Computer ScienceExperience of Designing and Applications of CAD Systems in Microelectronics. Proceedings of the VI-th International Conference. CADSM 2001 (IEEE Cat. No.01 EX473)
- 2001

In this case, interval optimization problem with interval objective function is considered, which involves solving optimization problems on graphs on graphs under uncertainty.

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