MoL-2013-09: The Iterative Minimum Cost Spanning Tree Problem

MoL-2013-09: Bekius, Femke (2013) The Iterative Minimum Cost Spanning Tree Problem. [Report]

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Abstract

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 service from the source. We provide an algorithm for the iterative minimum cost spanning tree problem in order to connect the agents from the different rounds to the source in a minimal way. Moreover, we discuss the complexity of the algorithm. To divide the cost of the constructed network among the agents in a fair way we propose different charge rules. One class of charge rules is defined in such a way that the inefficiency of the network, caused by agents joining in different rounds, is equally divided among the agents who use the network. A second class of charge rules charges the incoming agents as much as possible such that previously connected agents can be reimbursed. However, we want to avoid that agents are better off by construction their own network. Furthermore, we prove that the charge rules satisfy several properties. This provides the basis for comparing the charge rules and allows for assessment of their fairness in a particular situation.

Item Type: Report
Report Nr: MoL-2013-09
Series Name: Master of Logic Thesis (MoL) Series
Year: 2013
Uncontrolled Keywords: Logic; Mathematics
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/898

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