Yet another distributed depth-first-search algorithm
Information Processing Letters
A hundred impossibility proofs for distributed computing
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
A modular technique for the design of efficient distributed leader finding algorithms
ACM Transactions on Programming Languages and Systems (TOPLAS)
A trade-off between information and communication in broadcast protocols
Journal of the ACM (JACM)
Introduction to distributed algorithms
Introduction to distributed algorithms
A SubLinear Time Distributed Algorithm for Minimum-Weight Spanning Trees
SIAM Journal on Computing
Improvements in the time complexity of two message-optimal election algorithms
Proceedings of the fourth annual ACM symposium on Principles of distributed computing
A Distributed Algorithm for Minimum-Weight Spanning Trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Time-message trade-offs for the weak unison problem
Nordic Journal of Computing
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Echo Algorithms: Depth Parallel Operations on General Graphs
IEEE Transactions on Software Engineering
Graph Traversal Techniques and the Maximum Flow Problem in Distributed Computation
IEEE Transactions on Software Engineering
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It is well known that, for most non-trivial problems (such as Election, Spanning-Tree Construction, Traversal, Broadcast, etc.), any generic solution requires at least Ω(m) messages in the worst case, where m is the number of links among the n entities. However, all the existing proofs of this fact assume that the network size (i.e., the parameters n and m) are not known to the protocol. A natural question arises whether this rather strong assumption, which is crucial for the proofs, is truly necessary for establishing a lower bound to these problems. In this paper we answer this question and prove that the Ω(m) bound is inherent for all these problems, as well as many more. In fact, we consider the class of global problems, that is those whose solution requires the involvement of every entity in the communication (sending or receiving messages). The relationship between n and m plays an important role in establishing the lower bound. We show that for most networks (where m ≤ 1/2 (n-2)(n-3)+1) a generic solution for any problem in this class requires at least m messages even if n, m, and the degree of each node are known. This result holds for almost all values of m (e.g., when 1/2(n - 2)(n - 3) + 1 m ≤ 1/2 (n - 1)(n - 2) + 1 the number of required messages is m-1), even if there is a single initiator and the entities have distinct identifiers, and both these facts are known. Moreover, the results hold even if the protocol can maintain a global view of the network. As the networks become more dense, namely the network approaches a complete graph, the number of required messages is gradually reduced. For extreme values of m (i.e., m = 1/2n(n - 1) - c 1/2 (n-1)(n-2)+1), where c ≥ 0 is constant, the lower bound gradually approaches Ω(n); this is understandable since we establish it for the single initiator scenario. However, we prove that in networks of such a size, single initiators problems such as Broadcast and Traversal can be solved with precisely that order of magnitude. This means that for those problems the knowledge of n and m generates a significant and sudden complexity drop from Θ(n2) to Θ(n).