Suppose each vertex in a graph \( G \) has a unit of information and that all the units must be collected at a vertex \( u \) in \( G \). Assuming that a vertex can receive (from its neighbors) an unlimited number of units at each discrete moment but can only send one at a time, find the shortest collection time, \( \operatorname{col}_u(G) \), needed to collect all the information at \( u \) and an optimal protocol that achieves this.
We derive lower and upper bounds for the problem, give a polynomial time algorithm in the general case, and a linear time algorithm for hypercubes.