Electing a leader in a synchronous ring
Journal of the ACM (JACM)
Log-logarithmic selection resolution protocols in a multiple access channel
SIAM Journal on Computing
Computing on an anonymous ring
Journal of the ACM (JACM)
Computing on an anonymous network
PODC '88 Proceedings of the seventh annual ACM Symposium on Principles of distributed computing
Better computing on the anonymous ring
Journal of Algorithms
A logspace algorithm for tree canonization (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Computing Boolean functions on anonymous networks
Information and Computation
Theoretical Computer Science
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Comparison of initial conditions for distributed algorithms on anonymous networks
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
Computing anonymously with arbitrary knowledge
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
An O(nlog n) Unidirectional Algorithm for the Circular Extrema Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Decentralized extrema-finding in circular configurations of processors
Communications of the ACM
Uniform Leader Election Protocols for Radio Networks
IEEE Transactions on Parallel and Distributed Systems
Efficient algorithms for leader election in radio networks
Proceedings of the twenty-first annual symposium on Principles of distributed computing
Universal traversal sequences with backtracking
Journal of Computer and System Sciences - Complexity 2001
Electing a Leader when Processor Identity Numbers are not Distinct (Extended Abstract)
Proceedings of the 3rd International Workshop on Distributed Algorithms
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Sorting Multisets in Anonymous Rings
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
Leader election in rings with nonunique labels
Fundamenta Informaticae
Undirected connectivity in log-space
Journal of the ACM (JACM)
Deterministic Rendezvous in Trees with Little Memory
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Electing a leader in the local computation model using mobile agents
AICCSA '08 Proceedings of the 2008 IEEE/ACS International Conference on Computer Systems and Applications
Leader Election in Ad Hoc Radio Networks: A Keen Ear Helps
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Randomized rendez-vous with limited memory
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Delays induce an exponential memory gap for rendezvous in trees
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
How to meet when you forget: log-space rendezvous in arbitrary graphs
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Constructing a map of an anonymous graph: applications of universal sequences
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Hi-index | 0.00 |
We study the minimum memory size with which nodes of a network have to be equipped, in order to solve deterministically the leader election problem. Nodes are unlabeled, but ports at each node have arbitrary fixed labelings which, together with the topology of the network, can create asymmetries to be exploited in leader election. We consider two versions of the leader election problem: strong LE in which exactly one leader has to be elected, if this is possible, while all nodes must terminate in a state "infeasible" otherwise, and weak LE, which differs from strong LE in that no requirement on the behavior of nodes is imposed, if leader election is impossible. Nodes are modeled as identical automata and we ask what is the minimum amount of memory of such an automaton to enable leader election. We show that logarithmic memory is optimal for leader election in the class of arbitrary connected graphs. Weak LE can be achieved with O(log n) bits of memory for all connected graphs with at most n nodes and strong LE can be achieved with O(log n) bits of memory for all connected graphs with exactly n nodes (none of these assumptions can be entirely removed). On the other hand, we show that Ω(log n) bits of memory are necessary to enable leader election even for the class of rings. By contrast we show that strong LE can be accomplished in the class of trees of maximum degree Δ using only O(log log Δ) bits of memory, without any additional information. This proves an exponential gap in memory requirements for leader election between the class of trees and the class of arbitrary graphs. Moreover, we prove that no automaton can solve the leader election problem for all trees, even in the weak form.