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 Anonymous Rings: Franklin Goes Probabilistic

We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size

Tree-based Algorithm to Find the k-th Value in Distributed Systems

In this paper, we study distributed algorithms for finding the k-th value in the decentralized systems. First we consider the case of circular configuration of processors where no processor knows the total number of participants. Later a network of arbitrary configuration is examined and a tree-based algorithm is proposed. The proposed algorithm requires O(N) messages and O(log N) rounds of message passing, where N is the number of nodes in the network

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

Two Lower Bounds In Asynchronous Distributed Computation

We introduce new techniques for deriving lower bounds on the message complexity in asynchronous distributed computation. These techniques combine the choice of specific patterns of communication delays and crossing sequence arguments with consideration of the speed of propagation of messages, together with careful counting of messages in different parts of the network. They enable us to prove the following results, settling two open problems: An Ω(n log* n) lower bound for the number of messages sent by an asynchronous algorithm for computing any nonconstant function on a bidirectional ring of n anonymous processors. An Ω(n log n) lower bound for the average number of messages sent by any maximum finding algorithm on a ring of n processors, in case n is known

Synchronization Algorithms for Multi-cores and Multiprocessors

A distributed system is a group of processors that do not allocate memory. As an alternative, each processor has its own local memory, and the processors communicate with one another through communication lines such as local-area or wide-area networks. The processors in a distributed system vary in size and function. Such systems may include small handheld or real-time devices, personal computers, workstations, and large mainframe computer systems. Distributed systems, will have their own set of unique challenges, including synchronizing data and creating sense of conflicts. Effective synchronization algorithms performance depends on runtime factors that are rigid to predict. The designers have protocols to employ the synchronization operation and waiting mechanisms to wait for synchronization delays. In this paper an effort is made to investigate synchronization algorithm that vigorously select waiting mechanisms and protocols in response to runtime factors so as to attain enhanced performance. DOI: 10.17762/ijritcc2321-8169.150615

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

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology