Some lower bound results for decentralized extrema-finding in rings of processors

AbstractWe consider the problem of finding the largest of a set of n uniquely numbered processors, arranged in a ring, by means of an asynchronous distributed algorithm without a central controller. Processors are identical, except for their unique number (identity). Using a technique of Frederickson and Lynch we show that arbitrary algorithms that solve this problem on rings where processors know the ring size cannot have a better worst-case number of messages than algorithms that use only comparisons between identities. We show a similar type of result for rings, where the ring size is not known. We use these results to answer a question, posed by Korach, Rotem, and Santoro in 1981 whether each extrema-finding algorithm that uses time n on a ring of n processors must use a quadratic number of messages; and to show a lower bound of 0.683 n log(n) on the worst-case number of messages for unidirectional rings with known ring size n. Also, we give a lower bound of 12n log(n) on the average number of messages for algorithms that use only comparisons on rings with known ring size n

Exact average message complexity values for distributed election on bidirectional rings of processors

International audienceConsider a distributed system of n processors arranged on a ring. All processors are labeled with distinct identity-numbers, but are otherwise identical. In this paper, we make use of combinatorial enumeration methods in permutations and derive the one and the same exact asymptotic value, lJ2nH,,+O(n), of the expected number of messages in both probabilistic and deterministicbidirectional variants of Chang-Roberts distributed election algorithm. This confirms the result of Bodlaender and van Leeuwen (1986) that distributed Ieader finding is indeed strictly more efficient on bidirectional rings of processors than on unidirectional ones

Leader election in synchronous networks

Worst, best and average number of messages and running time of leader election algorithms of different distributed systems are analyzed. Among others the known characterizations of the expected number of messages for LCR algorithm and of the worst number of messages of Hirschberg-Sinclair algorithm are improve

The Complexity of Sorting on Distributed Systems

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424National Science Foundation / MCS-821744

Leader Election : from higham-przytycka's algorithm to a gracefully degrading algorithm

The leader election problem consists in selecting a process (called leader) in a group of processes. Several leader election algorithms have been proposed in the past for ring networks, tree networks, fully connected networks or regular networks (such as tori and hypercubes). As far as ring networks are concerned, it has been shown that the number of messages that processes have to exchange to elect a leader is (n log n). The algorithm proposed by Higham and Przytycka is the best leader algorithm known so far for ring networks in terms of message complexity, which is 1.271 n log n + O(n). This algorithm uses round numbers and assumes that all processes start with the same round number. More precisely, when round numbers are not initially equal, the algorithm has runs that do not terminate. This paper presents an algorithm, based on Higham-Przytycka's technique, which allows processes to start with different round numbers. This extension is motivated by fault-tolerance with respect to initial values. While the algorithm always terminates, its message complexity is optimal, i.e., O(n log n), when the processes start with the same round number and increases up to O(n2) when all processes start with different round number values. We call graceful degradation this additional property that combines fault-tolerance (with respect to initial values) and efficiency

Average Case Behavior of Distributed Extrema-Finding Algorithms

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / MCS-8217445Eastman Kodak Compan