Sublinear Bounds for Randomized Leader Election
نویسندگان
چکیده
This paper concerns randomized leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete n-node networks that runs in O(1) rounds and (with high probability) uses only O( √ n log n) messages to elect a unique leader (with high probability). When considering the “explicit” variant of leader election where eventually every node knows the identity of the leader, our algorithm yields the asymptotically optimal bounds of O(1) rounds and O(n) messages. This algorithm is then extended to one solving leader election on any connected non-bipartite n-node graph G in O(τ(G)) time and O(τ(G) √ n log n) messages, where τ(G) is the mixing time of a random walk on G. The above result implies highly efficient (sublinear running time and messages) leader election algorithms for networks with small mixing times, such as expanders and hypercubes. In contrast, previous leader election algorithms had at least linear message complexity even in complete graphs. Moreover, super-linear message lower bounds are known for time-efficient deterministic leader election algorithms. Finally, we present an almost matching lower bound for randomized leader election, showing that Ω( √ n) messages are needed for any leader election algorithm that succeeds with probability at least 1/e + ε, for any small constant ε > 0. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.
منابع مشابه
Near Optimal Leader Election in Multi-Hop Radio Networks
We present distributed randomized leader election protocols for multi-hop radio networks that elect a leader in almost the same time TBC required for broadcasting a message. For the setting without collision detection, our algorithm runs with high probability in O(D log n D + log n) · min{log logn, log n D } rounds on any n-node network with diameter D. Since TBC = Θ(D log n D + log n) is a low...
متن کاملTwo Absolute Bounds for Distributed Bit Complexity
The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained there open. The first is to close the gap between the known upper and lower bounds, for electing a leader by two linked proce...
متن کاملAn Improved Leader Election Protocol in Multi-hop Radio Networks
This paper presents two randomized protocols for the problem of electing a \leader" among a set of nodes in an arbitrary multi-hop radio network. First, a variation of the leader election protocol by Bar-Yehuda et al. BGI87] is presented, in which the termination problem is addressed. Then, an eecient randomized leader election protocol in arbitrary multi-hop radio networks is presented. Our el...
متن کاملLeader Election Algorithms for Multi-channel Wireless Networks
We study the leader election problem in single-hop multichannel wireless networks with single-antenna radio nodes. The objective is to elect leaders for all channels on which one or more nodes in the network can operate. We assume that nodes do not have collision detection capability. In this paper, we propose three algorithms for leader election: one deterministic and two randomized. The deter...
متن کامل