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

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