Bounded-wait combining: constructing robust and high-throughput shared objects

Abstract

Shared counters are among the most basic coordination structures in distributed computing. Known implementations of shared counters are either blocking, non-linearizable, or have a sequential bottleneck. We present the first counter algorithm that is both linearizable, nonblocking, and can provably achieve high throughput in k-synchronous executions -executions in which process speeds vary by at most a constant factor k. The algorithm is based on a novel variation of the software combining paradigm that we call bounded-wait combining. It can thus be used to obtain implementations, possessing the same properties, of any object that supports combinable operations, such as a stack or a queue. Unlike previous combining algorithms where processes may have to wait for each other indefinitely, in the bounded-wait combining algorithm, a process only waits for other processes for a bounded period of time and then 'takes destiny in its own hands'.In order to reason rigorously about the parallelism attainable by our algorithm, we define a novel metric for measuring the throughput of shared objects, which we believe is interesting in its own right. We use this metric to prove that our algorithm achieves throughput of Ω(N/ log N ) in k-synchronous executions, where N is the number of processes that can participate in the algorithm.Our algorithm uses two tools that we believe may prove useful for obtaining highly parallel nonblocking implementation of additional objects. The first are "synchronous locks", locks that are respected by processes only in k-synchronous executions and are disregarded otherwise; the second are "pseduo-transactions" -a weakening of regular transactions that allows higher parallelism.

A scalable lock-free stack algorithm

“…Colvin and Grobes [5] presented a somewhat simplified version of our algorithm and proved its correctness by using the PVS [22] theorem prover. Recently, Hendler and Kutten [11] introduced bounded-wait combining, a technique by which asymptotically high-throughput lock-free linearizable implementations of objects that support combinable operations (such as counters, stacks, and queues) can be constructed.…”

A Dynamic Elimination-Combining Stack Algorithm

“…The collide function, presented in Figure 2-(d), implements the elimination-combining backoff algorithm performed after a multi-op fails on the central stack. 3 It receives as its input a pointer to the first multiOp record in a multi-op list. A delegate thread executing the function first registers by writing to its entry in the location array (line 46) a pointer to its multiOp structure, thus advertising itself to other threads that may access the elimination-combining layer .…”

“…Two key synchronization paradigms for the construction of scalable concurrent data-structures in general, and concurrent stacks in particular, are software combining [13,3,4] and elimination [1,10]. Eliminationbased concurrent data-structures allow operations with reverse semantics (such as push and pop stack operations) to "collide" and exchange values without having to access a central location.…”