Feb 2003 2nd IPTPS

Lighthouses for Scalable Distributed Location

Marcelo Pias UCLJon Crowcroft CL/Cambridge UniversitySteve Wilbur UCLTim Harris Cambridge UniversitySaleem Bhatti UCL

Feb 2003 2nd IPTPS

Motivation

Self-organizing content addressable storage

Networked Games

Resources discovery (e.g. GRID)

Finesse failure of “triangle inequality”

Questions:

a. “Could we characterise network proximity in a scalable model by

computing node locations with a set of coordinates?

b. Could this model help these systems in selecting topologically close peers?”

Feb 2003 2nd IPTPS

Problem

Constraint: only a few distance measures are available.

General Space ‘M’

Objects {x1,x2,…,xn} = Network nodes

Distance Measures (e.g. propagation delay)

x1

x2

x3

Mapping

Vector Space ‘V’

Points {v1,v2,…,vn}

Distances Preserved

v2

v1

v3

Feb 2003 2nd IPTPS

Pivoting

Lighthouse

Multiple local bases (decentralised)

Transition Matrix

Global basis

Same well-known ‘pivot nodes’

Scalability problem (bottlenecks/node failure)

Pivoting

Distance from a given node to pre-selected pivots {p1,…,pn}

Feb 2003 2nd IPTPS

n6

n4 n

5

n2

n1

n3

G = {n1n2, , n1n3 }

{n 4,n 5,

, n6 }

REQ Lig

hthouse

s

Distance Measure(e.g. Ping)

1. Finding Lighthouses

n7

Feb 2003 2nd IPTPS

n6

n4 n

5

n2

n1

n3

G = {n1n2, , n1n3 }

2. Local Basis Coordinates

L = {n4n5, , n4n6}

n7

Feb 2003 2nd IPTPS

n6

n4

n5

n2

n1

n3

G = {n1n2, , n1n3 }

3. Host Coordinates

n7 = c1 . l1 + c2 . l2

l1 = {n4n5 }

l2 = {n4n6 }

c1 . l

1

c2 . l2

Feb 2003 2nd IPTPS

n6

n4

n5

n2

n1

n3

G = {n1n2, , n1n3 }

4. Transition Matrix

n7 = c1 . l1 + c2 . l2

l1 = {n4n5 }

l2 = {n4n6 }

n7 maintains a transition matrix

P = [ [n4n5] [n4n6] ]

Feb 2003 2nd IPTPS

Initial Experiments

Objectives

Accuracy: how close the predicted distance is to the real distance measured

Data (delay measures available at http://www-2.cs.cmu.edu/~eugeneng/research)

Probe matrix: mutual distance measures between 19 probes around the World

Target matrix: delay measures between 869 hosts and the 19 probes

Dimensions Distance Function

Number Probes

3 L2 (Euclidean) 4

Table I: Key Parameters

Feb 2003 2nd IPTPS

Initial Results

Feb 2003 2nd IPTPS

Open Questions

Network Performance Metrics

Propagation delay so far. What about other metrics?

E.g. power,cost,txput… Distance Function

Metric or non-metric?

E.g. power metric might reflect attenuation

What about obstacles (can we reflect shadows)? Curse of Dimensionality

How many dimensions?

Crovella reports <= 7 works very well on large internet

What would work for other metric in ad hoc wireless Choosing Lighthouses

Do they form a linear independent basis?

How could Lighthouse be incorporated in DHT/DT systems?

Feb 2003 2nd IPTPS

Conclusions

Lighthouse

maps objects and their distance measures onto points in a k-dimensional vector space.

It avoids the scalability problem presented by systems that rely on ‘well-known’ pivots as reference points (e.g. GNP, Binning, Beaconing)

It computes coordinates as accurate as GNP

Future work

Investigate the ‘open questions’