1 / 13

Know thy neighbor’s neighbor: Better Routing for Skip-Graphs and Small Worlds

Know thy neighbor’s neighbor: Better Routing for Skip-Graphs and Small Worlds. Moni Nao, Udi Wieder. Αθανασόπουλος Διονύσης Καμωνά Λαμπρινή Φωτιάδου Αικατερίνη. Introduction. Aim : Propose an approach for routing in DTH’s which is better than greedy routing

quasar
Download Presentation

Know thy neighbor’s neighbor: Better Routing for Skip-Graphs and Small Worlds

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Know thy neighbor’s neighbor: Better Routing for Skip-Graphs and Small Worlds Moni Nao, Udi Wieder Αθανασόπουλος Διονύσης Καμωνά Λαμπρινή Φωτιάδου Αικατερίνη

  2. Introduction • Aim: Propose an approach for routing in DTH’s which is better than greedy routing • Greedy routing: move to the node that minimizes the L1 distance to the target. • Examples:Chord, Skip Nets, Skip Graphs,

  3. Greedy Routing Advantages • Simplicity: Easy to understand and implement • Fault Tolerance: as long as each node has some edge towards the target, it is guaranteed that the message will reach its destination • Locality in the key space: Message do not “wander” in the key space

  4. Greedy Routing • Why use something else? Not degree optimal • Greedy -> O(logn) != Optimal -> O(logn/loglogn) • NoN Greedy algorithm (Neighbor-of-Neighbor) Enjoys the advantages of greedy, while being degree optimal

  5. Kleinberg’s model [2000] • People  points on a two dimensional grid • Grid edges (short range) • One long range contact chosen with the Harmonic distribution • probability of (u,v) proportional to 1/d(u,v)2 • Degree of each node Θ(logn) • Naturally generalizes to q long range links

  6. Small Worlds • d-dimensional grid • Each edge (u,v) is connected with probality ||u-v||-d • Degree of each node Θ(logn) • Originates from long range percolation model • Shares structural properties with some popular randomizedP2P networks: R-Chord, R-Hypercube, Skip Lists…

  7. The NoN-Greedy Algorithm

  8. The NoN-Greedy Algorithm • Step (2) is implemented by putting all z in a search tree. Search time = O(log(k2)) • K=logn => Search time = O(loglogn)

  9. Greedy vs NoN-Greedy • 224 nodes • 150 executions for each size • 34% improvement

  10. The NoN-Greedy Algorithm • Phase1: the message is sent to a neighbor whose neighbor is close to the target • Phase2-greedy step: the message moves to the neighbor of the neighbor

  11. Fault Tolerance – Optimistic Scenario • A node knows if its lists are updated • If not updated performs a greedy step • P(NoN)= ½ • P(Greedy)= ½

  12. Fault Tolerance – Pessimistic Scenario • Node is unaware that its list are up-to-date • With probability ½ the edge (w,z) no longer exists • i) w performs a greedy step • ii) w performs a NoN step

  13. NoN - Chord • Make Chord resemble the Small World • Each node x is connected to logn nodes y0,y1,y2… • yi is a random point in [x+2i, x+2i+1] • Path length= O(logn/loglogn)

More Related