P2P Streaming Monitor using

Global Network Positioning (GNP) System

Sin Wang Chiu

swchiuaa@ust.hk

ABSTRACT

As P2P network architecture is being more and more popular, more and more

researches are done on P2P network. P2P streaming is an important use of P2P

network technology. For more in depth knowledge and research on P2P streaming, we

need to know about the topology of the network in order to optimize the P2P

streaming network. To achieve this, we need a monitor system to monitor the situation

of the network to facilitate the development of the P2P streaming system. In this paper,

we propose to use the Global Network Positioning (GNP) system to implement a

monitor system.

I. Introduction

GNP system is an algorithm proposed by Ng and Zhang of Carnegie Mellon

University which is published in the paper named “Predicting Internet Network

Distance with Coordinates-Based Approaches”. (1)

GNP put the network topology in a

mathematical coordinate system (e.g. 2-D Cartesian coordinate system). The reason

behind is that coordinates property can be easily calculated and implemented (e.g.

network distance). In this paper, the algorithm propose will be slightly different from

the one in proposed in Ng and Zhang’s paper in which no fixed landmarks will be

used.

II. Algorithm

Consider a set of measured distance dNa, Nb where Na and Nb represent 2 different

nodes in the P2P network. In this algorithm, we are going generate a set of

coordinates S1, S2… Sn which have a set of generated distance of d’Sa, Sb. The set of

generated coordinates is obtained by minimizing the error between dN1, N2 and d’S1, S2.

Thus ,it can be solved as a generic multi-dimensional global minimization problem by

Simplex method proposed by Nelder and Mead in a paper titled “A simplex method

for function minimization”.(2)

Several method in measuring the error can be used and simple square error is used in

the paper, i.e. we are going to minimize the sum of the function below:

(dNa, Nb - d’Sa, Sb)2

where 1<=a,b<=n

Here, we denote the function we are going to minimize as objective function, f. We

use the simplex proposed by Nelder and Mean to minimize the function f.

III. Progress

The algorithm is implemented in C++ in order to test its efficiency and accuracy.

Testing is done by feeding human generated data into the system.

IV. Result

Key:

generated solution

Format: x1 y1 x2 y2 x3 y3……..

Input matrix (may not be symmetric)

Input matrix in symmetric form (by taking average)

Generated distance matrix

Test 1:

Test case:

Input: symmetric distance matrix in 101 order

Output:

A set of coordinates, accuracy can be evaluated by the

generated distance matrix.

The set of solution approximately correct in the sense

that the large distance is represent as a large distance in

the result distance matrix.

Test 2:

Test case:

Input: asymmetric distance matrix in 101

order

Output:

A set of coordinates, accuracy can be evaluated by the

generated distance matrix.

The set of solution approximately correct in the sense

that the large distance is represent as a large distance in

the result distance matrix.

Test 3:

Test case:

Input: asymmetric distance

matrix in 102

order

Output:

A set of coordinates, accuracy

can be evaluated by the

generated distance matrix.

The set of solution

approximately correct in the

sense that the large distance is

represent as a large distance

in the result distance matrix.

Evaluation of results:

As shown above, the system is now able to generate coordinates with an input

distance matrix. The coordinates is acceptable in the sense that it can distinguish

between large distances and small distances. However, the large and small is not

proportional to the input distances, i.e. the distances are in in scale.

Accuracy should be improved by adjusting the constants used in the algorithm.

V. Future Development:

1. Adjust the constants used in the algorithm in order to improve accuracy and

minimize the runtime. This may also help in improving the scaling issue

mentioned above

2. As the input matrix must be full in this implementation in which the situation is

nearly impossible in the real P2P network. Algorithm should be adjusted in order

to accept incomplete input distance matrix.

3. The input distance matrix is stored in the form of 2D-array in the current design

which is a waste of memory in the real situation. It is because in the real P2P

network, the input distance matrix is quite impossible to be full, i.e. most of the

space in the 2D array is wasted. A list-based storage can be used in order to

reduce the use of memory.

4. The runtime is quite long for the algorithm such that if there are more and more

nodes, the runtime may increase to an impractical long time. The algorithm should

be fine tune in order to make it possible to be used in a large scale monitor system.

VI. Summary

GNP system is a network coordinating system which can be easily implemented and

used in the real world. It can provide approximately correct coordinates for the use in

calculation and network optimizing.

However, the fine tune of the system is not that easy and need to be investigate in the

future.

VII. References

(1) T. S. Eugene Ng and Hui Zhang, "Predicting Internet Network Distance with

Coordinates-Based Approaches", INFOCOM'02, New York, NY, June 2002

(2) J.A. Nelder and R.Mead, “A simplex method for function minimization,” Computer

Journal, vol. 7, pp. 308–313, 1965.