Message-Efficient Uniform Timed Reliable Broadcast

In distributed database systems, atomic commitment protocols ensure that transactions leave the database in a consistent state even if failures occur during transactions. As shown by Babaoglu and Toueg, the heart of the atomic commitment problem is equivalent to uniform timed reliable broadcast (UTRB), which is a broadcast primitive that provides the following guarantees [Babaoglu and Toueg]: B1 (Validity): If a correct process broadcasts a message m, then all correct processes eventually deliver m. B2 (Integrity): For any message m, each process delivers m at most once, and only if some process actually broadcasts m. B3 (∆ b-Timeliness): There exists a known constant ∆ b such that if the broadcast of m is initiated at real-time t, no process delivers m after real-time t+∆ b. B4 (Uniform Agreement): If any process (correct or not) delivers a message m, then all correct processes eventually deliver m. We consider two complexity metrics for UTRB algorithms: time and number of messages. Let N be the number of processes. Assume that communication is FIFO and reliable, and each message is received within δ time units (as measured in real-time) after being sent. Local overhead of communication is captured by a parameter τ: after a process sends a set of at most N-1 messages to different processes, τ time units elapse before more messages can be sent. It is easy to devise a time-optimal UTRB protocol, e.g., UTRB1 of [Babaoglu and Toueg], which works as follows. Each process relays every message it receives to all other processes before delivering the message; thus, if any process delivers a message, then that message must have been sent to all processes. Let f denote the total number of processes that crash during an execution of the protocol, then the worst-case time complexity of UTRB1 is only (f+1)δ, but the worst-case number of messages is (N-1) 2. What about a message-optimal algorithm then? The most message-efficient algorithm in the literature is UTRB2 [Babaoglu and Toueg], which uses three types of messages: MSG announces a broadcast, DLV causes a delivery, and REQ requests help. The initial broadcaster constructs a list of processes called cohorts that will cooperate in performing the broadcast. The first process on this list is the broadcaster itself. To tolerate the failure up to F processes, the list contains F+1 distinct process name. This list, along with the index of the current cohort is included in MSG …