Leader Election Algorithm Research Articles

Linear election in pancake graphs

Pancake graphs have been proposed as an attractive alternative to hypercube networks. They have a smaller diameter and a lower degree. They also have a hierarchical structure which can be exploited in designing algorithms. In this paper, we propose a leader election algorithm for oriented pancake graphs. The algorithm has a message complexity that is linear in the order of the graph.

Randomized leader election

We present an efficient randomized algorithm for leader election in large-scale distributed systems. The proposed algorithm is optimal in message complexity (O(n) for a set of n total processes), has round complexity logarithmic in the number of processes in the system, and provides high probabilistic guarantees on the election of a unique leader. The algorithm relies on a balls and bins abstraction and works in two phases. The main novelty of the work is in the first phase where the number of contending processes is reduced in a controlled manner. Probabilistic quorums are used to determine a winner in the second phase. We discuss, in detail, the synchronous version of the algorithm, provide extensions to an asynchronous version and examine the impact of failures.

MDVM System Concept, Paging Latency and Round-2 Randomized Leader Election Algorithm in SG

The future trend in the computing paradigm is marked by mobile computing based on mobile-client/server architecture connected by wireless communication network. However, the mobile computing systems have limitations because of the resource-thin mobile clients operating on battery power. The MDVM system allows the mobile clients to utilize memory and CPU resources of Server-Groups (SG) to overcome the resource limitations of clients in order to support the high-end mobile applications such as, m-commerce and virtual organization (VO). In this paper the concept of MDVM system and the architecture of cellular network containing the SG are discussed. A round-2 randomized distributed algorithm is proposed to elect a unique leader and co-leader of the SG. The algorithm is free from any assumption about network topology, buffer space limitations and is based on dynamically elected coordinators eliminating single point of failure. The algorithm is implemented in distributed system setup and the network-paging latency values of wired and wireless networks are measured experimentally. The experimental results demonstrate that in most cases the algorithm successfully terminates in first round and the possibility of second round execution decreases significantly with the increase in the size of SG (|<I>Na</I>|). The overall message complexity of the algorithm is O(|<I>Na</I>|). The comparative study of network-paging latencies indicates that 3G/4G mobile communication systems would support the realization of MDVM system.

Cost distribution of the Chang–Roberts leader election algorithm and related problems

A detailed probabilistic analysis is proposed of the total number of messages of the Chang–Roberts leader election algorithm. The cost is shown to be closely related to the total path length in random recursive trees, the total left-path length in increasing binary trees and the major cost of an in situ permutation algorithm.

Quasi-optimal energy-efficient leader election algorithms in radio networks

Radio networks (RN) are distributed systems ( ad hoc networks ) consisting in n ≥ 2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection ( no-CD ) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, respectively. Both randomized protocols are shown to elect a leader within O ( log ( n ) ) expected time, with no station being awake for more than O ( log log ( n ) ) time slots (such algorithms are said to be energy-efficient ). Therefore, a new class of efficient algorithms is set up that match the Ω ( log ( n ) ) time lower-bound established by Kushilevitz and Mansour [E. Kushilevitz, Y. Mansour, An Ω ( D log ( N / D ) ) lower-bound for broadcast in radio networks, SIAM J. Comp. 27 (1998) 702–712).].

Asymptotic analysis of a leader election algorithm

Itai and Rodeh showed that, on the average, the communication of a leader election algorithm takes no more than LN bits, where L ≃ 2.441716 and N denotes the size of the ring. We give a precise asymptotic analysis of the average number of rounds M ( n ) required by the algorithm, proving for example that M ( ∞ ) ≔ lim n → ∞ M ( n ) = 2.441715879 … , where n is the number of starting candidates in the election. Accurate asymptotic expressions of the second moment M ( 2 ) ( n ) of the discrete random variable at hand, its probability distribution, and the generalization to all moments are given. Corresponding asymptotic expansions ( n → ∞ ) are provided for sufficiently large j, where j counts the number of rounds. Our numerical results show that all computations perfectly fit the observed values. Finally, we investigate the generalization to probability t / n , where t is a non-negative real parameter. The real function M ( ∞ , t ) ≔ lim n → ∞ M ( n , t ) is shown to admit one unique minimum M ( ∞ , t * ) on the real segment ( 0 , 2 ) . Furthermore, the variations of M ( ∞ , t ) on the whole real line are also studied in detail.

SELF-STABILIZING ANONYMOUS LEADER ELECTION IN A TREE

We propose a new self-stabilizing anonymous leader election algorithm in a tree graph. We show the correctness of the protocol and show that the protocol terminates in O(n4) time starting from any arbitrary initial state. The protocol can elect either a leaf node or a non leaf node (starting from the same initial state) depending on the behavior of the daemon. The protocol generalizes the result in [1] and at the same time is much simpler and terminates in polynomial number of moves.

A probabilistic analysis of a leader election algorithm

A leader election algorithm is an elimination process that divides recursively into tow subgroups an initial group of n items, eliminates one subgroup and continues the procedure until a subgroup is of size 1. In this paper the biased case is analyzed. We are interested in the cost of the algorithm e. the number of operations needed until the algorithm stops. Using a probabilistic approach, the asymptotic behavior of the algorithm is shown to be related to the behavior of a hitting time of two random sequences on [0,1].

Variations on Itai-Rodeh Leader Election for Anonymous Rings and their Analysis in PRISM

We present two probabilistic leader election algorithms for anonymous uni- directional rings with FIFO channels, based on an algorithm from Itai and Rodeh (Itai and Rodeh 1981). In contrast to the Itai-Rodeh algorithm, our algorithms are finite-state. So they can be analyzed using explicit state space exploration; we used the probabilistic model checker PRISM to verify, for rings up to size four, that even- tually a unique leader is elected with probability one. Furthermore, we give a manual correctness proof for each algorithm.

Leader election in hierarchical star network

We propose a new leader election algorithm for the oriented hierarchical star networks that has linear message complexity.

Simplifying Itai-Rodeh Leader Election for Anonymous Rings

We present two probabilistic leader election algorithms for anonymous unidirectional rings with FIFO channels, based on an algorithm from Itai and Rodeh [A. Itai and M. Rodeh. Symmetry breaking in distributive networks. In Proc. FOCS'81, pp. 150–158. IEEE Computer Society, 1981]. In contrast to the Itai-Rodeh algorithm, our algorithms are finite-state. So they can be analyzed using explicit state space exploration; we used the probabilistic model checker PRISM to verify, for rings up to size four, that eventually a unique leader is elected with probability one.

Leader election in oriented star graphs

AbstractLeader election in a network plays an important role in the area of distributed algorithm design. Structural properties of the network as well as presence of direction on the edges of the network greatly affects the complexity of the leader election problem, which is primarily measured by the message complexity of the protocol. Our purpose in the present article is to adapt the existing distributed match making concepts to design a linear time leader election algorithm for star graphs. Star graphs have been extensively studied as an attractive alternative for the well‐known hypercubes for network design. Linear election algorithms for oriented hypercubes is known; no such algorithm exists for oriented star graphs. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(2), 169–179 2005

이동 에드 혹 네트워크를 위한 제어노드 선택 알로리즘 및 성능 평가

이동 에드 혹 네트워크(Mobile Ad hoc Network)에서는 노드들이 pear-to-pear 레벨에서 무선 채널을 통하여 대화 한다. 노드들은 지리적으로 이동이 자유로우며 무선 채널들은 영역 내에서 약하게 결합된다. 그리고 노드들이 자유롭게 이동할 수 있기 때문에 고정된 네트워크의 형태가 존재하지 않는다. 따라서 노드들간의 데이터 교관이나 노드간의 통신을 관리하기 위해서 리더 노드(Leader Node)가 필요하다. 본 논문에서는 이웃 노드간에만 대화가 허용되는 이동 에드 혹 네트워크를 위한 효율적인 리더 노드 선택 알고리즘을 소개한다. 그리고 시뮬레이션을 통한 알고리즘의 성능 평가 결과를 보인다. 본 논문에서 소개한 알고리즘은 노드들의 이동에 영향을 받지 않고 최소한의 무선 자원만을 사용하는 효율적이고 실용적인 알고리즘이다. Nodes communicate through wireless channels under peer-to-peer level in ad-hoc mobile networks. The nodes are free to move around in a geographical area and are loose]y bounded by the transmission range of the wireless channels. Also, a node is completely free to move around, there is no fixed final topology. Hence, to manage the inter-node communication and data exchange among them a leader node is required. In this paper we introduce an efficient leader election algorithm for mobile ad hoc networks where inter-node communication is allowed only among the neighboring nodes. Furthermore we present the result of performance evaluation through simulation. The algorithm is efficient and practical since it uses least amount of wireless resources and does not affect the movement of the nodes.

Location Information-Aided Task-Oriented Self-Organization of Ad-Hoc Sensor Systems

A novel task-oriented self-organization algorithm that accounts for mostly location-dependent tasks and heterogeneous sensors inherent in dense ad-hoc sensor systems is proposed. It forms a sensor group for an announced task by sequentially selecting the best matched sensors using a leader election algorithm and a residual task calculation algorithm. To improve the associated communication overhead, the sensor node location information is used in task broadcasting, thus confining the algorithm implementation to a dynamically maintained contributor group which comprises of those sensors which may contribute to the task. Sensor localization is based on a refinement of an algorithm in which utilizes only the neighborhood information of each sensor node corresponding to its each preset radio transmission power level. The proposed self-organization algorithm and how various system parameters affect its performance are examined via extensive simulations. In a densely deployed sensor system, when the refined localization scheme is demonstrated to achieve very good localization, the proposed self-organization algorithm consistently yields a sensor group that covers the announced task.

Fun with FireWire: A Comparative Study of Formal Verification Methods Applied to the IEEE 1394 Root Contention Protocol

Abstract. The IEEE 1394 Root Contention Protocol is an industrial leader election algorithm for two processes in which probability, real time and parameters play an important role. This protocol has been analysed in various case studies, using a variety of verification and analysis methods. In this paper, we survey and compare several of these case studies.

Token-Based Self-Stabilizing Uniform Algorithms

This work focuses on self-stabilizing algorithms for mutual exclusion and leader election—two fundamental tasks for distributed systems. Self-stabilizing systems are able to recover by themselves, regaining their consistency from any initial or intermediary faulty configuration. The proposed algorithms are designed for any directed, anonymous network and stabilize under any distributed scheduler. The keystones of the algorithms are the token management and routing policies. In order to break the network symmetry, randomization is used. The space complexity is O((D++D−)(log(snd(n))+2)) where n is the network size, snd(n) is the smallest integer that does not divide n and D+ and D− are the maximal out and in degree, respectively. It should be noted that snd(n) is constant on the average and equals 2 on odd-size networks.

Asymptotic and numerical studies of the leader election algorithm

A leader is to be elected from n people using the following algorithm. Each person flips a coin. Those people who wind up with tails (which occurs with probability p, 0 < p < 1) move on to the next stage. Those with heads are eliminated. Let Hn denote the number of stages needed until there is a single winner. We analyze the moments and the probability distribution of Hn. In the symmetric model we have an unbiased coin with p = 1/2; in the asymmetric model p ≠ 1/2. We analyze these models asymptotically, for n → ∞, using a variety of analytical and numerical approaches. This leads to simple derivations of some existing results, as well as some new results for the asymmetric case. Our analysis makes some assumptions about the forms of various asymptotic expansions as well as their asymptotic matching.

Algorithms for Leader Election by Cellular Automata

We present two cellular algorithms, in O(n) and respectively in O(w2), for the leader election problem on finite connected rings F and respectively finite connected subsets of Zd, of eccentricity w, for any fixed d. The problem consists of finding an algorithm such that when setting the elements of F to a special state, and all the others to a state #, the cellular automaton iterates a finite number of steps and sets only one precise element of F to a special state called leader state, and all the others to a different state. We describe the algorithms in detail, give their proofs and complexities, and discuss the possible extensions.

Heuristics for Hierarchical Partitioning with Application to Model Checking

Given a collection of connected components, it is often desired to cluster together<br />parts of strong correspondence, yielding a hierarchical structure. We address the <br />automation of this process and apply heuristics to battle the combinatorial and <br />computational complexity.<br />We define a cost function that captures the quality of a structure relative to the<br />connections and favors shallow structures with a low degree of branching. Finding<br />a structure with minimal cost is shown to be NP-complete. We present a greedy<br />polynomial-time algorithm that creates an approximate good solution incrementally<br />by local evaluation of a heuristic function. We compare some simple heuristic <br />functions and argue for one based on four criteria: The number of enclosed connections,<br />the number of components, the number of touched connections and the depth of the structure.<br />We report on an application in the context of formal verication, where our <br />algorithm serves as a preprocessor for a temporal scaling technique, called \"ext" heuristic<br /> [AW99]. The latter is applicable in enumerative reachability analysis and is included<br />in the recent version of the Mocha model checking tool.<br />We demonstrate performance and benefits of our method and use an asynchronous<br />parity computer, a standard leader election algorithm, and an opinion poll protocol as<br />case studies.

Verification of a Leader Election Protocol: Formal Methods Applied to IEEE 1394

The IEEE 1394 high performance serial multimedia bus protocol allows several components to communicate with each other at high speed. In this paper we present a formal model and verification of a leader election algorithm that forms the core of the tree identify phase of the physical layer of the 1394 protocol. We describe the algorithm formally in the I/O automata model of Lynch and Tuttle, and verify that for an arbitrary tree topology exactly one leader is elected. A large part of our verification has been checked mechanically with PVS, a verification system for higher-order logic.