Bounds on Contention Management Algorithms

We present two new algorithms for contention management in transactional memory, the deterministic algorithm

CommitRounds

and the randomized algorithm

RandomizedRounds

. Our randomized algorithm is efficient: in some notorious problem instances (e.g., dining philosophers) it is exponentially faster than prior work from a worst case perspective. Both algorithms are (i) local and (ii) starvation-free. Our algorithms are local because they do not use global synchronization data structures (e.g., a shared counter), hence they do not introduce additional resource conflicts which eventually might limit scalability. Our algorithms are starvation-free because each transaction is guaranteed to complete. Prior work sometimes features either (i) or (ii), but not both. To analyze our algorithms (from a worst case perspective) we introduce a new measure of complexity that depends on the number of actual conflicts only. In addition, we show that even a non-constant approximation of the length of an optimal (shortest) schedule of a set of transactions is NP-hard – even if all transactions are known in advance and do not alter their resource requirements. Furthermore, in case the needed resources of a transaction varies over time, such that for a transaction the number of conflicting transactions increases by a factor

k

, the competitive ratio of any contention manager is Ω(

k

) for

$k<\sqrt{m}$

, where

m

denotes the number of cores.