1. Feb 2003 2 nd IPTPS Lighthouses for Scalable Distributed Location Marcelo Pias UCL Jon Crowcroft CL/Cambridge University Steve Wilbur UCL Tim Harris Cambridge University Saleem Bhatti UCL

2. Feb 2003 2 nd 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?”

3. Feb 2003 2 nd 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) x1x1 x2x2 x3x3 Mapping Vector Space ‘V’ Points {v1,v2,…,vn} Distances Preserved v2v2 v1v1 v3v3

4. Feb 2003 2 nd 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}

5. Feb 2003 2 nd IPTPS n6n6 n4n4 n5n5 n2n2 n1n1 n3n3 G = {n 1 n 2,, n 1 n 3 } {n 4,n 5,, n 6 }REQ Lighthouses Distance Measure (e.g. Ping) 1. Finding Lighthouses n7n7

6. Feb 2003 2 nd IPTPS n6n6 n4n4 n5n5 n2n2 n1n1 n3n3 G = {n 1 n 2,, n 1 n 3 } 2. Local Basis Coordinates L = {n 4 n 5,, n 4 n 6 } n7n7

7. Feb 2003 2 nd IPTPS n6n6 n4n4 n5n5 n2n2 n1n1 n3n3 G = {n 1 n 2,, n 1 n 3 } 3. Host Coordinates n 7 = c 1. l 1 + c 2. l 2 l 1 = {n 4 n 5 } l 2 = {n 4 n 6 } c 1. l 1 c 2. l 2

8. Feb 2003 2 nd IPTPS n6n6 n4n4 n5n5 n2n2 n1n1 n3n3 G = {n 1 n 2,, n 1 n 3 } 4. Transition Matrix n 7 = c 1. l 1 + c 2. l 2 l 1 = {n 4 n 5 } l 2 = {n 4 n 6 } n 7 maintains a transition matrix P = [ [ n 4 n 5 ] [ n 4 n 6 ] ]

9. Feb 2003 2 nd 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 DimensionsDistance FunctionNumber Probes 3L 2 (Euclidean)4 Table I: Key Parameters

10. Feb 2003 2 nd IPTPS Initial Results

11. Feb 2003 2 nd 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?

12. Feb 2003 2 nd 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’