The “wait-free hierarchy ” classifies multiprocessor synchronization primitives according to their power to solve consensus. The classification is based on assigning a number n to each synchronization primitive, where n is the maximal number of processes for which deterministic wait-free consensus can be solved using instances of the primitive and read write registers. Conditional synchronization primitives, such as compare-and-swap and load-linked/store-conditional, can implement deterministic wait-free consensus for any number of processes (they have consensus number ∞), and are thus considered to be among the strongest synchronization primitives. To some extent because of that, compare-and-swap and load-linked/store-conditional have became the synchronization primitives of choice, and have been implemented in hardware in many multiprocessor architectures. This paper shows that, though they are strong in the context of consensus, conditional synchronization primitives are not efficient in terms of memory space for implementing many key objects. Our results hold for starvation-free implementations of mutual exclusion, and for wait-free implementations of a large class of concurrent objects, that we call Visible(n). Roughly, Visible(n) is a class that includes all objects that support some operation that must perform a “visible”

We prove an Ω(n log n) lower bound on the number of nonbusywaiting memory accesses by any deterministic algorithm solving n process mutual exclusion that communicates via shared registers. The cost of the algorithm is measured in the state change cost model, a variation of the cache coherent model. Our bound is tight in this model. We introduce a novel information theoretic proof technique. We first establish a lower bound on the information needed by processes to solve mutual exclusion. Then we relate the amount of information processes can acquire through shared memory accesses to the cost they incur. We believe our proof technique is flexible and intuitive, and may be applied to a variety of other problems and system models.

. This paper details the design of a scalable algorithm for the mutual exclusion problem. Starting by inserting a redundant assignment into Peterson's algorithm for two processes, we derive another algorithm that uses only local spins, i.e., a process busy-waits only on locally accessible shared variables. The new two-process algorithm is then adapted to serve as a building block of the complete tournament-like algorithm; the adaptation is such that the entire algorithm still uses only local spins, which is crucial for scalability. We consider the simplicity of the algorithm and its derivation to be the main contributions of this paper. Keywords: local spins, mutual exclusion, read/write atomicity, refinement, scalability. 1 Introduction New solutions seem never to stop emerging for the mutual exclusion problem, despite its relatively old age. 1 A new solution is proposed either to meet newly conceived criteria or to improve over previous ones with respect to certain tangible or le...

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A simple code transformation is presented that reduces the space complexity of Yang and Anderson's local-spin mutual exclusion algorithm. In this algorithm, only atomic read and write instructions are used; each process generates (log N) remote memory references per lock request, where N is the number of processes. The space complexity of the transformed algorithm is (N), which is clearly optimal. Its time complexity is (log N), like the original.

Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. A recent proof [9] established an Ω(log N) lower bound on the number of RMRs incurred by processes as they enter and exit the critical section, matching an upper bound by Yang and Anderson [18]. Both these bounds apply for algorithms that only use read and write operations. The lower bound of [9] only holds for deterministic algorithms, however; the question of whether randomized mutual exclusion algorithms, using reads and writes only, can achieve sub-logarithmic expected RMR complexity remained open. This paper answers this question in the affirmative. We present two strong-adversary [8] randomized local-spin mutual exclusion algorithms. In both algorithms, processes incur O(log N / log log N) expected RMRs per passage in every execution. Our first algorithm has sub-optimal worstcase RMR complexity of O ( (log N / log log N) 2). Our second algorithm is a variant of the first that can be combined with a deterministic algorithm, such as [18], to obtain O(log N) worst-case RMR complexity. The combined algorithm thus achieves sub-logarithmic expected RMR complexity while maintaining optimal worst-case RMR complexity. Our upper bounds apply for both the cache coherent (CC) and the distributed shared memory (DSM) models.

We study the complexity of renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct names from a given namespace. We prove an individual lower bound of Ω(k) process steps for deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. This bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic fetch-and-increment registers, queues and stacks. The proof of the bound is interesting in its own right, for it relies on the first reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement our individual bound with a global lower bound of Ω(k log(k/c)) on the total step complexity of renaming into a namespace of size ck, for any c ≥ 1. This applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter and fetch-and-increment implementations, all tight within logarithmic factors. 1

Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. A mutual exclusion algorithm is adaptive to point contention, if its RMR complexity is a function of the maximum number of processes concurrently executing their entry, critical, or exit section. In the best prior art deterministic adaptive mutual exclusion algorithm, presented by Kim and Anderson [22], a process performs O ( min(k, log N) ) RMRs as it enters and exits its critical section, where k is point contention and N is the number of processes in the system. Kim and Anderson also proved that a deterministic algorithm with o(k) RMR complexity does not exist [21]. However, they describe a randomized mutual exclusion algorithm that has O(log k) expected RMR complexity against an oblivious adversary. All these results apply for algorithms that use only atomic read and write operations. We present a randomized adaptive mutual exclusion algorithms with O(log k / log log k) expected amortized RMR complexity, even against a strong adversary, for the cachecoherent shared memory read/write model. Using techniques similar to those used in [17], our algorithm can be adapted for the distributed shared memory read/write model. This establishes that sub-logarithmic adaptive mutual exclusion, using reads and writes only, is possible.

Abstract Mutual exclusion is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on local-spin algorithms and uses the remote memory references (RMRs) metric. Attiya, Hendler, and Woelfel (40th STOC, 2008) established an �(log N) lower bound on the number of RMRs incurred by processes as they enter and exit the critical section, where N is the number of processes in the system. This matches the upper bound of Yang and Anderson (Distrib. Comput. 9(1):51–60, 1995). The upper and lower bounds apply for algorithms that only use read and write operations. The lower bound of Attiya et al., however, only holds for deterministic algorithms. The question of whether randomized mutual exclusion algorithms, using reads and writes only, can achieve sub-logarithmic expected RMR complexity remained open. We answer this question in the affirmative by presenting starvation-free randomized mutual exclusion algorithms for the cache coherent (CC) and the distributed shared memory (DSM) model that have sub-logarithmic expected RMR complexity against the strong adversary. More specifically, each process incurs an expected number of O(log N / log log N) RMRs per passage through the entry and exit sections, while in the worst case the number of RMRs is O(log N). P. Woelfel was supported by NSERC.

Abstract We consider the time complexity of shared-memory mutual exclusion algorithms based on reads, writes, and comparison primitives under the remote-memory-reference (RMR) time measure. For asynchronous systems, a lower bound of \Omega (log N / log log N) RMRs per critical-section entry has been established in previous work, where N is the number of processes. Also, algorithms with O(log N) time complexity are known. Thus, for algorithms in this class, logarithmic or near-logarithmic RMR time complexity is fundamentally required.