Cooperation in the Absence of Communication

In the setting where the Omni-Do (and Do-All) problem needs to be solved by distributed message-passing processors there exists a trade-off between computation and communication: both resources must be managed to decrease redundant computation and to ensure efficient computational progress. In this chapter we specifically examine the extreme situation of collaboration without communication. That is, we consider the extent to which efficient collaboration is possible if all resources are directed to computation at the expense of communication. Of course there are also cases where such an ex- treme situation is not a matter of choice: the network may fail, the mobile nodes may have intermittent connectivity, and when communication is un- available it may take a long time to (re)establish connectivity. The results summarized in this section precisely characterize the ability of distributed agents to collaborate on a known collection of independent tasks by means of local scheduling decisions that require no communication and that achieve low redundant work in task executions. Such scheduling solutions exhibit an interesting connection between the distributed collaboration problem and the mathematical design theory. The lower bounds presented here along with the randomized and deterministic schedule constructions show the limitations on such low-redundancy cooperation and show that schedules with near-optimal redundancy can be efficiently constructed by processors working in isolation.