Dartmouth College Computer Science Technical Report series 
CS home TR home TR search TR listserv 

By author:  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z  
By number:  2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986 
Abstract:
The notion of distributed functional monitoring was recently introduced by Cormode, Muthukrishnan and Yi 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 \sigma, the union of the k streams. The goal is to minimize the number of bits communicated by a protocol that correctly monitors f(\sigma), 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(\sigma) \leq \tau(1  \epsilon) and 1 whenever f(\sigma) \geq \tau. Following Cormode et al., we term this the (k, f, \tau, \epsilon) 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., F_0, F_1, F_2. Importantly, these functions are monotone. Here, we further advance the study of such problems, proving three new classes of results. First, we prove new lower bounds on this problem when f = F_p, for several values of p. Second, we study the effect of nonmonotonicity of f on our ability to give nontrivial monitoring protocols, by considering f = F_p with deletions allowed, as well as f = H, the empirical Shannon entropy of a stream. Third, we provide nontrivial monitoring protocols when f is either H, or any of a related class of entropy functions (Tsallis entropies). These are the first nontrivial algorithms for distributed monitoring of nonmonotone functions.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Chrisil Arackaparambil,
Joshua Brody, and
Amit Chakrabarti,
"Functional Monitoring Without Monotonicity."
Dartmouth Computer Science Technical Report TR2008639,
December 2008.
Notify me about new tech reports.
To receive paper copy of a report, by mail, send your address and the TR number to reports AT cs.dartmouth.edu
Copyright notice: The documents contained in this server are included by the contributing authors as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.
Technical reports collection maintained by David Kotz.