Combining Funnels: A Dynamic Approach to Software Combining

We enhance the well established software combining synchronization technique to create combining funnels Previous software combiningmethods used a statically assigned tree whose depth was logarithmic in the total number of processors in the system On shared memory multiprocessors the new method allows to dynamically build combining trees with depth logarithmic in the actual number of processors concurrently accessing the data structure The structure is comprised from a series of combining layers through which processor s requests are funneled These layers use randomization instead of a rigid tree structure to allow processors to nd part ners for combining By using an adaptive scheme the funnel can change width and depth to accommodate di erent access frequencies without requiring global agree ment as to its size Rather processors choose parameters of the protocol privately making this scheme very simple to implement and tune When we add an elim ination mechanism Touitou to the funnel structure the randomly constructed tree is transformed into a forest of disjoint and on average shallower trees of requests thus enhancing the level of parallelism and decreasing latency We present two new linearizable combining funnel based data structures a fetch and add object and a stack We study the performance of these structures by benchmarking them against the most e cient software implementations of fetch and add and stacks known to date combining trees and elimination trees on a simulated shared memory multiprocessor using Proteus Our empirical data shows that combining funnel based fetch and add outperforms combining trees of xed height by as much as In fact even compared to combining trees optimized for a given load funnel performance is the same or better Elimination trees which are not linearizable are faster than funnels under highest load but as load drops combining funnels adapt their size giving them a lead in latency A preliminary version of this work appeared in Principals of Distributed Computing PODC Supported by NSF grant CCR A grant from the Israel Ministry of Science and a grant from the Israel National Academy of Sciences Contact Author E mail shanir math tau ac il Supported by an Israeli Ministry of Science Eshkol Scholarship