Team member reallocation via tree pruning

This paper considers the task reallocation problem, where k agents are to be extracted from a coordinated group of N agents in order to perform a new task. The interaction between the team members and the cost associated with this interaction are represented by a weighted graph. Consider a group of N robots organized in a formation, the graph is the monitoring graph which represents the sensorial capabilities of the robots, i.e., which robot can sense the other and al what cost. Following this example, the team member reallocation problem this paper deals with is the extraction of k robots from the group in order to acquire a new target, while minimizing the cost of the interaction of the remaining group. In general, the method proposed here shifts the utility from the team member itself to the interaction between the members, and calculates the reallocation according to this interaction utility. We found that this can be done optimally by a deterministic polynomial time algorithm under several constraints, the first constraint is that k = script O sign(log N). We describe several other domains in which this method is applicable.