The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations

Fair cost-sharing methods for the minimum spanning tree game

A Metaheuristic Algorithm for the Minimum Routing Cost Spanning Tree Problem

The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start ...

The Iterative Minimum Cost Spanning Tree Problem

The minimum cost spanning tree problem consists in constructing a network of minimum cost that connects all agents to the source and distributes the cost among the agents in a fair way. We develop a framework for the iterative minimum cost spanning tree problem. In the iterative setting, agents arrive over time and desire to be connected to a source in different rounds in order to receive a ser...

On Continuous Cost Sharing Solutions for Minimum Cost Spanning Tree Problems

A review of continuous cost sharing solutions for the minimum cost spanning tree problem is proposed, with a particular focus on the folk and Kar solutions. We compare the characterizations proposed, helped by some new results on equivalencies between sets of properties.

Computation of the Shapley Value of Minimum Cost Spanning Tree Games: #P-Hardness and Polynomial Cases

We show that computing the Shapley value of minimum cost spanning tree games is #P-hard even if the cost functions are restricted to be {0, 1}-valued. The proof is by a reduction from counting the number of minimum 2-terminal vertex cuts of an undirected graph, which is #P-complete. We also investigate minimum cost spanning tree games whose Shapley values can be computed in polynomial time. We ...