Distributed Cardinality Estimation In Anonymous Networks
Abstract
We consider estimation of network cardinality by distributed anonymous strategies relying on statistical
inference methods. In particular, we focus on the relative Mean Square Error (MSE) of Maximum
Likelihood (ML) estimators based on either the maximum or the average of M-dimensional vectors
randomly generated at each node. In the case of continuous probability distributions, we show that the
relative MSE achieved by the max-based strategy decreases as 1/M, independently of the used
distribution, while that of the average-based estimator scales approximately as 2/M. We then introduce a
novel strategy based on the average of M-dimensional vectors locally generated from Bernoulli random
variables. In this case, the ML estimator, which is the Least Common Multiple (LCM) of the denominators
of the irreducible fractions corresponding to the M elements of the average vector, leads to an MSE which
goes exponentially to zero as M increases. We then discuss the effects of finite-precision arithmetics in
practical dynamic implementations. Numerical experiments reveal that the MSE of the strategy based on
Bernoulli trials is two order of magnitude smaller than that based on continuous random variables, at a
price of one order of magnitude slower convergence time.
Existing system
We consider estimation of network cardinality by distributed anonymous strategies relying on statistical
inference methods. In particular, we focus on the relative Mean Square Error (MSE) of Maximum
Likelihood (ML) estimators based on either the maximum or the average of M-dimensional vectors
randomly generated at each node. In the case of continuous probability distributions, we show that the
relative MSE achieved by the max-based strategy decreases as 1/M, independently of the used
distribution, while that of the average-based estimator scales approximately as 2/M.
Proposed system
We then introduce a novel strategy based on the average of M-dimensional vectors locally generated
from Bernoulli random variables. In this case, the ML estimator, which is the Least Common Multiple
(LCM) of the denominators of the irreducible fractions corresponding to the M elements of the average
vector, leads to an MSE which goes exponentially to zero as M increases. We then discuss the effects of
finite-precision arithmetics in practical dynamic implementations. Numerical experiments reveal that the
MSE of the strategy based on Bernoulli trials is two order of magnitude smaller than that based on
continuous random variables, at a price of one order of magnitude slower convergence time.
SYSTEM CONFIGURATION:HARDWARE CONFIGURATION:-
Further Details Contact: A Vinay 9030333433, 08772261612
Email: takeoffstudentprojects@gmail.com | www.takeoffprojects.com
 Processor
 Speed
-
Pentium –IV
1.1 Ghz
 RAM
-
256 MB(min)
 Hard Disk
-
20 GB
 Key Board
-
Standard Windows Keyboard
 Mouse
-
 Monitor
Two or Three Button Mouse
-
SVGA
SOFTWARE CONFIGURATION:-
 Operating System
: Windows XP
 Programming Language
: JAVA
 Java Version
: JDK 1.6 & above.
Further Details Contact: A Vinay 9030333433, 08772261612
Email: takeoffstudentprojects@gmail.com | www.takeoffprojects.com