|M.Sc Student||Kaplan Yaniv|
|Subject||Lower Bounds for Adaptive Collect and Related Objects|
|Department||Department of Computer Science||Supervisor||Professor Hagit Attiya|
Adaptive algorithms, whose step complexity adjusts to the number of active processes, are attractive for situations in which the number of participating processes is highly variable. This thesis studies the number and type of multi-writer registers that are needed for adaptive algorithms.
We prove that if a collect algorithm is f-adaptive to total contention, namely, its step complexity is f(k), where k is the number of processes that ever took a step, then it uses Ω(f-1(n)) multi-writer registers, where n is the total number of processes in the system.
Furthermore, we show that competition for the underlying registers is inherent for adaptive collect algorithms. We consider c-write registers, to which at most c processes can be concurrently about to write. Special attention is given to concurrent-write registers, the case c=n where any amount of competition is allowed, and exclusive-write registers, the case c=1 where no competition is allowed.
A collect algorithm that is f-adaptive to point contention, namely, its step complexity is f(k), where k is the maximum number of simultaneously active processes, is shown to require Ω (f-1(n/c)) concurrent-write registers, even if an unlimited number of c-write registers are available. A smaller lower bound is also obtained in this situation for collect algorithms that are f-adaptive to total contention.
Finally, we present lower bounds on the step complexity in solo executions (i.e., without any contention), when only c-write registers are used: for weak test&set objects we present an Ω ((log n)/(log c + loglog n)) lower bound, while for collect and sensitive objects the lower bound is Ω ((n-1)/c).