1998
DOI: 10.1137/s0097539794261118
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Abstract: This paper considers the question of identifying the parameters governing the behavior of fundamental global network problems. Many papers on distributed network algorithms consider the task of optimizing the running time successful when an O(n) bound is achieved on an n-vertex network. We propose that a more sensitive parameter is the network's diameter Diam. This is demonstrated in the paper by providing a distributed Minimum-weight Spanning Tree algorithm whose time complexity is sub-linear in n , but linea… Show more

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Cited by 142 publications
(112 citation statements)
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“…it is straightforward to see, even guaranteed that G is either a |V |-cycle or a |V |-path, not all edges can determine if they are cut edges in less than |V |/2 − 2 rounds. One term for this property is existentially optimal, due to Garay, Kutten and Peleg [12]. However, as Thurimella's algorithm [36] showed, there are some graphs on which Θ(V ) time is not asymptotically optimal.…”
Section: Existing Resultsmentioning
confidence: 99%
“…it is straightforward to see, even guaranteed that G is either a |V |-cycle or a |V |-path, not all edges can determine if they are cut edges in less than |V |/2 − 2 rounds. One term for this property is existentially optimal, due to Garay, Kutten and Peleg [12]. However, as Thurimella's algorithm [36] showed, there are some graphs on which Θ(V ) time is not asymptotically optimal.…”
Section: Existing Resultsmentioning
confidence: 99%
“…These classical distributed algorithms are oriented towards minimizing the total number of messages in general networks, and their time complexity is inherently Ω(log n), even when run on fully connected graphs. The model we use in this paper is a special case of the model studied in [7,12,10]: in these papers, each message has O(log n) bits, but the fully connected graph is not directly considered. The best previously known upper bound for fully connected graphs in this model is O(log n) communication rounds.…”
Section: Related Workmentioning
confidence: 99%
“…The asynchrony of the computational entities means that the algorithm must work regardless of the time required for each computation or movement, which is finite but a priori unknown (i.e., determined by an adversary); however, the time complexity of the algorithm is measured only over those executions where time delays are unitary (i.e., determined by a synchronous scheduler), as traditional in distributed computing (e.g., [12,18,23]). …”
Section: Main Contributionsmentioning
confidence: 99%
“…The amount of time between the earliest start time of the protocol by any agent and the time all the agents that started the protocol have terminated the execution of protocol. Since the system is asynchronous, when evaluating the time complexity we will employ ideal time; i.e., we will assume that it time delays are unitary (e.g., see [12,18,23]). …”
Section: Definitions and Notationsmentioning
confidence: 99%