Consensus Halving for Sets of Items

Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both equally. Prior work shows that, when is represented by an interval, consensus with at most n cuts always exists but hard compute even for agents simple valuation functions. In this paper, we study in natural setting which consists set items without linear ordering. For and additively separable utilities, present polynomial-time algorithm computes show are almost surely necessary agents’ utilities randomly generated. On other hand, class monotonic already becomes polynomial parity argument, directed version–hard. Furthermore, compare contrast more general k-splitting, wish divide k possibly unequal ratios provide some consequences our results on computing small agreeable sets.