Functional Monitoring without Monotonicity

The notion of distributed functional monitoring was recently introduced by Cormode, Muthukrishnan and Yi [CMY08] to initiate a formal study of the communication cost of certain fundamental problems arising in distributed systems, especially sensor networks. In this model, each of k sites reads a stream of tokens and is in communication with a central coordinator, who wishes to continuously monitor some function f of , the union of the k streams. The goal is to minimize the number of bits communicated by a protocol that correctly monitors f (), to within some small error. As in previous work, we focus on a threshold version of the problem, where the coordinator's task is simply to maintain a single output bit, which is 0 whenever f () (1-) and 1 whenever f () . Following Cormode et al., we term this the (k, f, , ) functional monitoring problem. In previous work, some upper and lower bounds were obtained for this problem, with f being a frequency moment function, e.g., F0, F1, F2...

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Chrisil Arackaparambil, Joshua Brody, Amit Chakrabarti
• Keywords: Cormode Et Al, Functional Monitoring Problem, ICALP 2009, Nontrivial Monitoring Protocols, Theoretical Computer Science