Multiagent MST Cover: Pleasing All Optimally via A Simple Voting Rule

Bo Li, Xiaowei Wu, Chenyang Xu, Ruilong Zhang

Abstract:

Given a connected graph on whose edges we can build roads to connect the nodes, a number
of agents hold possibly different perspectives on which edges should be selected by assigning
different edge weights. Our task is to build a minimum number of roads so that every agent has
a spanning tree in the built subgraph whose weight is the same as a minimum spanning tree
in the original graph. We first show that this problem is NP-hard and does not admit better
than ((1 − o(1)) ln k)-approximation polynomial-time algorithms unless P = NP, where k is the
number of agents. We then give a simple voting algorithm with an optimal approximation ratio.
Moreover, our algorithm only needs to access the agents’ rankings on the edges. Finally, we
extend our results to submodular objective functions and Matroid rank constraints.