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Concurrent broadcast involves the dissemination of a database, consisting of messages initially distributed among the nodes of a network, so that a copy of the entire database eventually resides at each node. One application is the dissemination of network status information for adaptive routing in a communications network. This paper examines the time complexity and communication complexity of several distributed procedures for concurrent broadcast. The procedures do not use information depending on the network topology. The worst-case time complexity of a flooding procedure for concurrent broadcast is shown to be linear in the number of nodes plus the number of messages, and no other procedure for concurrent broadcast has a better worst-case time complexity. A variant of flooding is proposed to eliminate redundant message receipts from the flooding process by real-time signaling between neighbors concerning messages residing at each. This variant can reduce communication complexity, while having a worst-case time complexity similar in form to that of the flooding procedure. Special properties of concurrent broadcast in a tree are also given. The present time complexity results can be used to bound the time during which inconsistent databases may reside at different nodes, to evaluate and compare procedures for (or including) concurrent broadcast, and to schedule a sequence of instances of concurrent broadcast so that the instances do not overlap and there is no need for sequence numbers.