Post-mortem black-box correctness tests for basic parallel data structures

Abstract

Operations on basic data structures such as queues, priority queues, stacks, and counters can dominate the execution time of a parallel program due to their frequency and their coordination and contention overheads. There are considerable performance payoffs in developing highly-optimized, asynchronous, distributed, cache-conscious, parallel implementations of such data structures. Such implementations may employ a variety of tricks to reduce latencies and avoid serial bottlenecks, as long as the semantics of the data structure are preserved. The complexity of the implementation and the difficulty in reasoning about asynchronous systems increases concerns regarding possible bugs in the implementation. In this paper, we consider black box procedures for testing whether a parallel data structure behaved correctly. We present the first systematic study of algorithms and hardness results for such testing procedures, focusing on queues, priority queues, stacks, and counters, under various important scenarios. Our results demonstrate the importance of selecting test data such that distinct values are inserted into the data structure (as appropriate). In such cases, we present an O(n) time algorithm for testing linearizable queues, an O(nlog n) time algorithm for testing linearizable priority queues, and an O(np’) time algorithm for testing non-linearizable queues, where n is the number of data structure operations and p is the number of processors. In contrast, we show that testing such data structures for executions with arbitrary input values is NP-complete. Our results also help clarify the thresholds between scenarios that admit polynomial time solutions and those that are NPcomplete. Our algorithms are the first nontrivial algorithms for these problems. *Bell Laboratories, Lucent Technologies, Room 2A-341, 600 Mountain Avenue, Murray Hill NJ 07974. gibbons@research.bell-labs.com +Dept. of Comp uter Science, University of California, Santa Barbara CA 93106. bruno@cs.ucsb.edu. This work was performed while the author was visiting Bell Labs. *AT&T Labs Research, Florham Park NJ 07932. phillips@research.att.com P,amission to makr digital or hard copies oral1 07 part oCthis WN’~ fi)r pcrsonal or classroom use is granted without fee provided that COPiCs are not mac{e or distributed for profit or commercial advatltage and that copies bear this notice alld Ihe full citation 011 the first page. To COPY otherwise, to republish, to post on seners 01’ to redistchute to lists. requires prior spccitic permission and/or a fee. SPAA ‘99 Saint Malo, France Cop,,,@ ACM 1999 I-581 13-124-0/99/06...$5.00