its frequency, fx = fx +1 else insert with frequency fx = 1 and error εx = wcur - 1 N = N + 1 Delete step Iterate over D and remove every element x with fx + εx ≤ wcur Output: elements in D with Example 8 1 2 2 3 5 5 1 1 2 3 3 3 3 1 2 0 1 1 3 5 input stream ε=0.2 w1 w4 w3 w2 1 2 2 3 5 w1 Delete items with fx + εx ≤ 1 1 2 3 5 1 0 2 0 1 0 1 0 f1 ε1 f2 ε2 f3 ε3 f5 ε5 ??? Vasiliki Kalavri | Example 8 1 2 2 3 5 5 1 1 2 3 3 3 3 1 2 0 1 1 3 5 input stream ε=0.2 w1 w4 w3 w2 1 2 2 3 5 w1 Delete items with fx + εx ≤ 1 1 2 3 5 1 0 2 0 1 0 1 0 f1 ε1 f2 ε2 f3 ε3 f5 ε5 ??? Vasiliki Kalavri |

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broadcast fashion. 11 12 Brokers vs. Databases • DBs keep data until explicitly deleted while MBs delete messages once consumed. • Use a database for long-term data storage! • MBs assume a small working in-memory brokers • Multiple consumers with different processing speeds: reading a message doesn't delete it • Coarse-grained load balancing: assign different partitions to different consumers • Limits

if (prevTemp == 0.0 || r.temperature < prevTemp) { // temperature decreased; delete current timer ctx.timerService().deleteProcessingTimeTimer(curTimer) } else if

memory footprint poly-logarithmic in the stream size • Low time: fast update and query times • Delete-proof: synopses can handle both insertions and deletions in an update stream • Composable: synopses

relation R contains a stream element whenever tuple s is in R(τ) − R(τ − 1). • Dstream (for “delete stream”) applied to relation R contains a stream element whenever tuple s is in R(τ − 1)

bits in the filter: • Increment the corresponding counter every time an element is added • To delete an element, decrease its corresponding counters and unset the corresponding bit of the counter falls