Adaptive and efficient mutual exclusion (extended abstract)

Abstract

A distributed algorithm is adaptive if its performance depends on k, the number of processes that are concurrently active during the algorithm execution (rather than on n, the total number of processes). This paper presents adaptive algorithm for mutual exclusion using only read and write operations.The worst case step complexity cannot be a measure for the performance of mutual exclusion algorithms, because it is always unbounded in the presence of contention. Therefore, a number of different parameters are used to measure the algorithm's performance: The remote step complexity is the maximal number of steps performed by a process where a wait is counted as one step. The system response time is the time interval between subsequent entries to the critical section, where one time unit is the minimal interval in which every active process performs at least one step.The algorithm presented here has O(k) remote step complexity and O(log k) system response time, where k is the point contention. The space complexity of this algorithm is O(nN), where N is the range of processes' names.The space complexity of all previously known adaptive algorithms for various long-rived problems depends on N. We present a technique that reduces the space complexity of our algorithm to be a function of n, while preserving the other performance measures of the algorithm.

Group mutual exclusion in O (log n ) RMR

“…The following claim will be crucial to complete the proof of Claim 3. Now we will prove that S = (s, d, s) at p [6]. We will prove this by further two cases depending upon the value of S at p [5].…”

“…As S = (s, d, s) at t, we first claim that S = (s, d, s) throughout the interval (p [5.1], t). This is true because for S to change at some time during the interval (p [5.1] Hence, S = (s, d, s) at p [6]. This means that p will execute Line 6 and set Out[s] = d at Line 7.…”

“…Research in exclusion algorithms and RMRs has led to design of many algorithms [1,2,5,6,10,14,17,19,25,26,29], lower bounds [3,7,11,13], and an understanding of the limitations of various shared memory primitives [7,11].…”

Constant RMR solutions to reader writer synchronization

“…The ideal goal is to design locking algorithms whose RMR complexity-the worst case number of remote memory references made by a process to enter and exit the CS once-is a constant, independent of the numbers of readers/writers attempting to acquire the lock. Research in this direction over the last two decades led to many algorithms [3,4,9,10,11,12,13,14,15,16,17], lower bounds [18,19,20,21], and an understanding of the limitations of various shared memory primitives [18,19]. The highlight is the design of constant RMR complexity mutual exclusion algorithms: Anderson's algorithm achieves constant RMR complexity for CC machines [3] and Mellor-Crummey and Scott's algorithm, which was awarded the Dijkstra Prize in 2006, achieves constant RMR complexity for both CC and DSM machines [4].…”