Anderson, R.J., Woll, H.: Wait-free Parallel Algorithms for the UnionFind Problem. Extended version of the STOC'91 paper of the authors, November 1 (1994)  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a wait free algorithm implemented using atomic compareand swap instructions yields better scalability on a large multiprocessor than a queue implemented with lock based synchronization. 1 Introduction Wait free data structures and algorithms have been an active area of research in recent years[3, 6, 12, 18], and have spawned a variety of applications[4, 8, 9] They have the desirable property that when multiple threads access a waitfree data structure, stalled threads cannot prevent other threads from making progress. This avoids a variety of problems encountered with lock based (blocking) ....

....an operation on a shared data structure is guaranteed to succeed in a finite number of steps, regardless of the actions of other threads. Examples of algorithms and data structures for which e#cient wait free implementations exist include queues[12, 18] double ended queues[6] and union find[3]. A variety of applications have been implemented using wait free algorithms and data structures. For example, because wait free data structures do not block, they are ideal for communication between execution contexts that run at di#erent priorities. This makes them useful for operating systems ....

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Richard J. Anderson and Heather Woll. Wait-free Parallel Algorithms for the Union-Find Problem. In ACM Symposium on Theory of Computing, 1991.

....fewer or much more permutations, then work of the instance must be signi cantly greater than the work that can be achieved. Details of the overview follow. We will present a tight bound on work of any instance of the AWT algorithm. Our lower bound generalizes the Lemma 5. 20 of Anderson and Woll [1]. The bound has an explicit constant which was hidden in the analysis given in the Lemma 5.20. The constant will play a paramount role in the analysis presented in the reminder of the section. Lemma 4.1. Work W of the AWT algorithm for p = q processors, h 1, q 2, and n = p cells, ....

Anderson, R.J., Woll, H.: Wait-free Parallel Algorithms for the Union-Find Problem. Extended version of the STOC'91 paper of the authors, November 1 (1994)

....a set of permutations so that a set of concurrent collect operations will take at most kn steps to be completed, for some k, independent of the scheduling of the processes steps. A rst step in this direction was made by Anderson and Woll in their elegant work on the certi ed write all problem [6] (see Section 2) Due to the requirement of freshness, our adversary is less constrained than the adversary in [6] where freshness is not an issue. Thus, we need additional insight into the combinatorial structure of the schedule. In particular, for this part of the proof we prove that if the ....

....for some k, independent of the scheduling of the processes steps. A rst step in this direction was made by Anderson and Woll in their elegant work on the certi ed write all problem [6] see Section 2) Due to the requirement of freshness, our adversary is less constrained than the adversary in [6], where freshness is not an issue. Thus, we need additional insight into the combinatorial structure of the schedule. In particular, for this part of the proof we prove that if the adversary has a short description, then there exists a good set of permutations. We then show that the adversary is ....

[Article contains additional citation context not shown here]

R. Anderson and H. Woll. Wait-free Parallel Algorithms for the Union-Find Problem. In Proc. 23rd ACM Symposium on Theory of Computing, pp. 370-380, 1991.

....in [47, 48] General synchronous PRAM simulations are impossible using bounded resources on asynchronous PRAMs. Buss et al. 27] show that some deterministic computations can be performed using subquadratic work, even when arbitrary asynchrony of PRAM processors is allowed. Anderson and Woll [8] also showed an efficient randomized solution for Write All , as well as the existence of Write All solutions with work O(N ) for P = N and any 0 that can be used with the models we define here. Finally, our work here deals with dynamic patterns of faults; for recent advances on coping ....

....or using a deterministic scheme that approximates a particular randomized scheme. Hashed allocation algorithms can be used in both restartable and non restartable failure models. Algorithm Y : this is an efficient determinization of a randomized algorithm that was defined by Anderson and Woll in [8]. We present this algorithm without analysis. Some experimental work suggests that the algorithm is a very efficient algorithm. The analysis of algorithm Y is stated as an open problem that shows an interesting linkage between group theory, combinatorics and multi processor scheduling. 3.2 Global ....

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R. Anderson and H. Woll, "Wait-Free Parallel Algorithms for the Union-Find Problem", Proc. of the 23rd ACM Symposium on Theory of Computing, pp. 370380, 1991. 125

....problem can be used iteratively to convert arbitrary sharedmemory computations into robust ones resilient to processor failures. This was the subject of papers by Kedem, Palem and Spirakis [13] Kedem, Palem, Rabin, and Raghunathan [11] Martel, Park, and Subramonian [15] and Anderson and Woll [1]. A logarithmic lower bound on time to solve write all deterministically was derived by Kedem, Palem, Raghunathan and Spirakis [12] and on expected time of randomized executions by Martel and Subramonian [14] Kanellakis and Shvartsman [9] proved a lower bound n log n= log log n) on available ....

R.J. Anderson, and H. Woll, Wait-Free Parallel Algorithms for the Union-Find Problem, in Proc. 23rd Symp. on Theory of Computing, 1991, pp. 370-380.

.... to the problem of Certified Write All, in which n processes have to write to n locations while individually being able to certify that all writes have occurred (indeed, the collect algorithm of Ajtai et al. AADW94] is largely based on a Certified WriteAll algorithm of Anderson and Woll [AW91] One can also think of the collect problem as an asynchronous version of the well known gossip problem [EM89] in which n persons wish to distribute n rumors among themselves with a minimum number of telephone calls; however, in the gossip problem, which persons communicate at each time is ....

R. Anderson and H. Woll. Wait-free parallel algorithms for the union-find problem. In Proc. 23rd ACM Symposium on Theory of Computing, pages 370--380, 1991.

....universal operations. His result, however, does not concern the efficiency of the implementations. Later papers on the implementation of concurrent data structures address their efficiency, and can be partitioned into three groups. The first group are implementations of specific data structures [15, 18, 3, 12]; the second group are implementations of multi word (k ary) operations from single word operations [2, 10, 20, 13] while the third group introduces general methods for implementing concurrent data structures [2, 9, 1, 6] Next we describe the works, elaborating on works from the second and third ....

....and Member operations, and uses the fetch add and two other primitives which can be viewed as simple cases of C S . Prakash, Lee and Johnson ( 18] present a non blocking implementation of a concurrent queue, supporting Enqueue and Dequeue operations, and using C S operations. Anderson and Woll ([3]) show a wait free implementation for a Union Find data structure, supporting Union, Find , and Sameset operations, and using C S operations. Israeli and Rappoport in [12] implemented a priority queue, which supports deleteMin and insert operations using a binary SC . Several papers present ....

R. J. Anderson and H. Woll, "Wait-Free parallel algorithms for the union-find problem ", Proceedings of the 23rd ACM Symposium on Theory of Computation, pages 370--380, May 1991.

....from other processors, thus sharing the work of reading the registers. Indeed, Saks, Shavit, and Woll [32] describe a collect algorithm that finishes quickly when most processors are running concurrently, and Ajtai et al. 3] observed that the Certified Write All algorithm of Anderson and Woll [5] could be modified in a straightforward way to solve the collect problem in O(n 3=2 log n) total operations. This is 2 a substantial improvement on an upper bound of n 2 , but still far from the best known lower bound of Omega Gamma n log n) 3] Repeated collects. The collect problem is ....

R. Anderson and H. Woll. Wait-free parallel algorithms for the UnionFind Problem. In Proc. 23rd ACM Symposium on Theory of Computing, pp. 370--380, 1991. 24

....problem can be used iteratively to convert arbitrary shared memory computations into robust ones resilient to processor failures. This was the subject of papers by Kedem, Palem and Spirakis [13] Kedem, Palem, Rabin, and Raghunathan [11] Martel, Park, and Subramonian [15] and Anderson and Woll [1]. A logarithmic lower bound on time to solve write all deterministically was derived by Kedem, Palem, Raghunathan and Spirakis [12] and on expected time of randomized executions by Martel and Subramonian [14] Kanellakis and Shvartsman [9] proved a lower bound (n log n= log log n) on available ....

R.J. Anderson, and H. Woll, Wait-Free Parallel Algorithms for the Union-Find Problem, in Proc. 23rd Symp. on Theory of Computing, 1991, pp. 370-380.

....cost measure any operational processor contributes a unit of work for any clock cycle during which it is operational, even if it is idle. Their approach to fault tolerance was continued in a series of papers, in particular those by Kanellakis, Michailidis, and Shvartsman [15] Anderson and Woll [1], Martel, Park, and Subramonian [24] Kedem, Palem, Rabin, and Raghunathan [18] and Kedem, Palem and Spirakis [20] Lower bounds on various kinds of algorithms solving write all were proved by Kedem, Palem, Raghunathan and Spirakis [19] Martel and Subramonian [23] Kanellakis and Shvartsman ....

R.J. Anderson, and H. Woll, Wait-Free Parallel Algorithms for the Union-Find Problem, in Proc. 23rd Symp. on Theory of Computing, 1991, pp. 370-380.

....technique which simulates a reliable PRAM on a faulty one. This idea was first introduced by Kanellakis and Shvartsman in [32] and later improved upon by Kedem et al. 33] Both of these results are for the fail stop model. In the general asynchronous model the results of Anderson and Woll [6] and Buss et al. 16] apply, and would mean an increase in the complexity of the sort to at least O(log 3 N ) and cost a multiplicative log N factor in memory. The method of Martel et al. 35] would also work, and would increase running time by only a log N factor. However, it supports only ....

....log N factor in memory. The method of Martel et al. 35] would also work, and would increase running time by only a log N factor. However, it supports only limited asynchrony through the use of the non standard FTS instruction. 1 The above simulations would not be efficient, as was noticed by [6], since they require synchronization at the end of every PRAM step. A previous result in fault tolerant sorting is given by Yen et al. 42] It employs the Batcher sorting network, giving a complexity of O(log 2 N ) This result supports only the fail stop failure model and requires non standard ....

[Article contains additional citation context not shown here]

Anderson, R. J., and Woll, H. Wait-free parallel algorithms for the union-find problem. In Proceedings of the 23rd Annual ACM Symposium on the Theory of Computing (New Orleans, LS, May 1991), B. Awerbuch, Ed., ACM Press, pp. 370-- 380.

....for a total cost of n 2 operations. However, the naive solution is not the best possible, as processors can learn values indirectly from other processors, thus sharing the work of reading the registers. Indeed, Ajtai et al. 3] observed that the Certified Write All algorithm of Anderson and Woll [5] could be modified in a straightforward way to solve the collect problem in O(n 3=2 log n) total operations. This is a substantial improvement on an upper bound of n 2 , but still far from the best known lower bound of Omega Gamma n log n) 3] Repeated collects. The collect problem is ....

R. Anderson and H. Woll. Wait-free parallel algorithms for the Union-Find Problem. In Proc. 23rd ACM Symposium on Theory of Computing, pp. 370--380, 1991.

....technique which simulates a reliable PRAM on a faulty one. This idea was first introduced by Kanellakis and Shvartsman in [22] and later improved upon by Kedem et al. 23] Both of these results are for the failstop model. In the general asynchronous model the results of Anderson and Woll [3] and Buss et al. 9] apply, and would mean an increase in the complexity of the sort to at least O(log 3 N ) and cost a multiplicative log N factor in memory. The method of Martel et al. 25] would also work, and would increase running time by only a log N factor. However, it supports only ....

....log N factor in memory. The method of Martel et al. 25] would also work, and would increase running time by only a log N factor. However, it supports only limited asynchrony through the use of the non standard FTS instruction. 1 The above simulations would not be efficient, as was noticed by [3], since they require synchronization at the end of every PRAM step. These results indicate the need to develop a sorting algorithm designed specifically for the wait free case. A previous result in fault tolerant sorting is given by Yen et al. 32] which employs the Batcher sorting network, ....

[Article contains additional citation context not shown here]

Anderson, R. J., and Woll, H. Wait-free parallel algorithms for the union-find problem. In Proceedings of the 23rd Annual ACM Symposium on the Theory of Computing (New Orleans, LS, May 1991), B. Awerbuch, Ed., ACM Press, pp. 370--380.

....set of permutations so that a set of concurrent collect operations will take at most kn steps to be completed, for some k, independent of the scheduling of the processes steps. A first step in this direction was made by Anderson and Woll in their elegant work on the certified write all problem [6] (see Section 2) Due to the requirement of freshness, our adversary is less constrained than the adversary in [6] where freshness is not an issue. Thus, we need additional insight into the combinatorial structure of the schedule. In particular, for this part of the proof we prove that if the ....

....some k, independent of the scheduling of the processes steps. A first step in this direction was made by Anderson and Woll in their elegant work on the certified write all problem [6] see Section 2) Due to the requirement of freshness, our adversary is less constrained than the adversary in [6], where freshness is not an issue. Thus, we need additional insight into the combinatorial structure of the schedule. In particular, for this part of the proof we prove that if the adversary has a short description, then there exists a good set of permutations. We then show that the adversary is ....

[Article contains additional citation context not shown here]

R. Anderson and H. Woll. Wait-free Parallel Algorithms for the Union-Find Problem. In Proc. 23rd ACM Symposium on Theory of Computing, pp. 370-- 380, 1991.

....an efficient solution that tolerates up to n Gamma 1 faults, and show how to use it to derive robust versions of parallel algorithms for a large class of interesting problems. Their original paper was followed by a number of papers that consider the problem in other shared memory models (see [AW, BR, KS2, KPRS, KPS, MSP]) There is an extensive literature on the related area of membership services (see, for example, CHT2, DMS, RB] for definitions and results in asynchronous systems) Group membership itself is a loosely defined term that generally describes the requirements on (1) the series of views held by a ....

R. J. Anderson and H. Woll, Wait-free Parallel Algorithms for the Union-Find Problem, Proc. 23rd Annual ACM STOC, pages 370-380, 1991.

....[19, 21] Valois [24, 25] and Michael and Scott [17] proposed non blocking implementations of concurrent link based queues. Treiber [22] proposed a non blocking implementation of concurrent link based stacks. Valois [26] proposed a non blocking implementation of linked lists. Anderson and Woll [3] proposed a non blocking solution to the union find problem. Simple non blocking centralized counters can be implemented using a fetch and add atomic primitive (if supported by hardware) or a read modify check write cycle using compare and swap or load linked store conditional. Performance ....

R. J. Anderson and H. Woll. Wait-Free Parallel Algorithms for the Union-Find Problem. In Proceedings of the Twenty-Third ACM Symposium on Theory of Computing, pages 370--380, May 1991.

....to Compare Swap, Herlihy [15] describes a methodology for converting synchronous implementations of data structure algorithms to non blocking and wait free implementations. Alemany and Felten [1] present techniques for improving the performance of Herlihy s protocol in practice. Anderson and Woll [2] use Compare Swap to design efficient asynchronous algorithms for the UnionFind problem. Heaps are often used to implement priority queues. Many researchers have examined the problem of concurrent access to priority queue structures such as skew trees, B trees, or 2 3 trees. Most existing ....

....as an array of pointers to nodes. Each node is a record consisting of the key, some flags, and a few auxiliary variables. By using Load Linked and Store Conditional on the pointer to a record, the algorithm can atomically check in the entire record. A similar strategy is used by Anderson and Woll [2] in their Union Find algorithms. In standard heap algorithms, both the delete min and insert operations are composed of a series of suboperations a new leaf is added to the heap, or the root key is removed and replaced by the key of one of the leaves, and a series of swaps is performed to ....

[Article contains additional citation context not shown here]

R. J. Anderson and H. Woll. Wait-free parallel algorithms for the unionfind problem. Technical Report 91-04-05, University of Washington, 1991. See also [3].

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R. Anderson and H. Woll, "Wait-Free Parallel Algorithms for the Union-Find Problem ", Proceedings of the 23rdACM Symposium on Theory of Computing , 1991, pp. 370-380. 261

....implementations using instructions that are stronger than simple reads and writes. Implementations of various types of queues have been presented by Lamport [53] by Herlihy and Wing [38] by Israeli and Rappoport [41] by Wing and Gong [81, 82] and byMichael and Scott [64] Anderson and Woll [15] and Lanin and Shasha [56] present implementations for various set operations. Valois presents lock free implementations for various data structures, including queues, lists, trees, and dictionaries [78, 79, 80] Finally, Massalin and Pu have implemented an entire operating system using lock free ....

R. Anderson and H. Woll. Wait-free parallel algorithms for the union-find problem. In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 370--380. ACM, August 1991.

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Anderson, R.J., Woll, H.: Wait-free Parallel Algorithms for the UnionFind Problem. Extended version of the STOC'91 paper of the authors, November 1 (1994)

No context found.

Anderson, R.J., Woll, H.: Wait-free Parallel Algorithms for the Union-Find Problem. Extended version of the STOC'91 paper of the authors, November 1 (1994)

No context found.

R. J. Anderson and H. Woll. Wait-free parallel algorithms for the union-find problem. In Proceedings of the ACM Symposium on the Theory of Computing, pages 370--380, 1991.

No context found.

R. Anderson and H. Woll. Wait-free parallel algorithms for the union-find problem. In Proceedings of the 23rd ACM Symposium on Theory of Computing, pages 370--380, 1991.

No context found.

Richard Anderson and Heather Woll. Wait-free parallel algorithms for the union-find problem. In Proceedings of the 23rd ACM Symposium on Theory of Computing, pages 370--380, 1991.

No context found.

R. J. Anderson and H. Woll. Wait-free parallel algorithms for the unionfind problem. In Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, pages 370--380, New Orleans, LA, May 1991.

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