# Path Optimality Conditions for Minimum Spanning Tree Problem with Uncertain Edge Weights

@article{Zhou2015PathOC, title={Path Optimality Conditions for Minimum Spanning Tree Problem with Uncertain Edge Weights}, author={Jian Zhou and Lu Chen and Ke Wang}, journal={Int. J. Uncertain. Fuzziness Knowl. Based Syst.}, year={2015}, volume={23}, pages={49-72} }

This paper investigates the uncertain minimum spanning tree (UMST) problem where the edge weights are assumed to be uncertain variables. In order to propose effective solving methods for the UMST problem, path optimality conditions as well as some equivalent definitions for two commonly used types of UMST, namely, uncertain expected minimum spanning tree (expected UMST) and uncertain α-minimum spanning tree (α-UMST), are discussed. It is shown that both the expected UMST problem and the α-UMST…

## Figures and Tables from this paper

## 35 Citations

### Uncertain Distribution-Minimum Spanning Tree Problem

- BusinessInt. J. Uncertain. Fuzziness Knowl. Based Syst.
- 2016

This paper studies the minimum spanning tree problem on a graph with uncertain edge weights, which are formulated as uncertain variables and shows that this problem can be effectively solved via the proposed deterministic graph transformation-based approach with the aid of the β-distribution-path optimality condition.

### Degree-constrained minimum spanning tree problem of uncertain random network

- Computer ScienceJ. Ambient Intell. Humaniz. Comput.
- 2017

In order to seek out the degree-constrained minimum spanning tree (DCST) closest to the ideal chance distribution, an uncertain random programming model is formulated and an algorithm is presented to solve the DCMST problem.

### Minimum spanning tree problem of uncertain random network

- MathematicsJ. Intell. Manuf.
- 2017

This paper focuses on the case where some weights are random variables and the others are uncertain variables, and a model is formulated to find a minimum spanning tree whose chance distribution is the closest to the ideal one.

### On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm

- Computer ScienceSymmetry
- 2022

Two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and the practical problem of optimizing the distribution of petroleum products was solved using a classical multi- objective solution technique, the epsilon-constraint method.

### Models for inverse minimum spanning tree problem with fuzzy edge weights

- Computer Science, BusinessJ. Intell. Fuzzy Syst.
- 2014

A fuzzy α-minimum spanning tree model and a credibility maximization model are presented to formulate the problem according to different decision criteria, and a fuzzy simulation for computing credibility is designed and embedded into a genetic algorithm to produce some hybrid intelligent algorithms.

### Minimum Spanning Tree with Uncertain Random Weights

- Mathematics, Business
- 2014

This paper considers the minimum spanning tree problem with uncertain random weights in an uncertain random network. The concept of uncertain random minimum spanning tree is initiated for minimum…

### An algorithmic approach for finding minimum spanning tree in a intuitionistic fuzzy graph

- Computer Science
- 2019

This paper modifies the classical Bor˚uvka’s algorithm to generate the IMST of fuzzy graph, which is the lifeline of any city and describes the utility of IMST in a water distribution network.

### Uncertain programming models for multi-objective shortest path problem with uncertain parameters

- Computer ScienceSoft Comput.
- 2020

An uncertain multi-objective shortest path problem (UMSPP) for a weighted connected directed graph (WCDG) where every edge weight is associated with two uncertain parameters: cost and time is presented.

### Entropy of Uncertain Random Variables wi h Application to Minimum Spanning Tree Problem

- MathematicsInt. J. Uncertain. Fuzziness Knowl. Based Syst.
- 2017

In this paper, a model is presented to formulate a minimum spanning tree problem with uncertain random edge weights involving a relative entropy chance distribution and some mathematical properties of this concept are investigated.

### ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH

- Mathematics
- 2017

Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The…

## References

SHOWING 1-10 OF 36 REFERENCES

### Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem

- Mathematics, Business
- 2013

An inverse minimum spanning tree problem makes the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In…

### Uncertain Quadratic Minimum Spanning Tree Problem

- MathematicsJ. Commun.
- 2014

It is shown that the problem of finding an uncertain quadratic - minimum spanning tree can be handled in the framework of the deterministic quadrato-minimum spanning tree problem requiring no particular solving methods.

### On Two-Stage Stochastic Minimum Spanning Trees

- Mathematics, Computer ScienceIPCO
- 2005

For the two-stage stochastic optimization formulation with finite scenarios, a simple iterative randomized rounding method on a natural LP formulation of the problem yields a nearly best-possible approximation algorithm.

### A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

- Computer ScienceThe Journal of Supercomputing
- 2010

A learning automata-based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown and the superiority of the proposed algorithm over the well-known existing methods both in terms of the number of samples and the running time of algorithm is shown.

### The minimum spanning tree problem with fuzzy costs

- Computer ScienceFuzzy Optim. Decis. Mak.
- 2008

The minimum spanning tree problem in a given connected graph is considered and Possibility theory is applied to characterize the optimality of edges of the graph and to choose a spanning tree under fuzzy costs.

### A near-optimal multicast scheme for mobile ad hoc networks using a hybrid genetic algorithm

- Computer Science20th International Conference on Advanced Information Networking and Applications - Volume 1 (AINA'06)
- 2006

### An Evolutionary Approach to Solve Minimum Spanning Tree Problem with Fuzzy Parameters

- Computer Science, BusinessInternational Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06)
- 2005

The minimum spanning tree problem with fuzzy parameters is studied and an exact algorithm is proposed to solve it. However, as this problem conveys the need of large number of comparisons, a genetic…