The Iterative Minimum Cost Spanning Tree Problem
Femke Bekius
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.
Keywords: Logic; Mathematics