idmaps: a global internet host distance estimation service p. francis, s. jamin, c. jin, y. jin, d....

IDMaps: A Global Internet Host Distance Estimation Service

P. Francis, S. Jamin, C. Jin, Y. Jin, D. Raz, Y. Shavitt, L.

Zhang

Presenter: Zhenying Liu

Contents

Background Goals Related work Architecture Performance Evaluation Conclusion

Background Increasing need to learn network

distances, bandwidth One method

Measure the distance by itself(ping, traceroute)

A useful general service: quick, efficient SONAR, Feb. 1996 HOPS(Host proximity Service) Need underlying measurement infrastructure

to provide distance measurements

Contents


IDMaps Internet Distance Map Service

To be underlying service that provides the distance information used by SONAR/HOPS

Goals Not near instantaneous information Determine roughly the best service given

technology constraints Consider whether there are applications for

which this level of service would be useful

Resulting Goals Separation of functions

Separation of IDMaps and the query/reply service

Distance Metrics Latency(round-trip delay)

useful, easy to provide Bandwidth

Useful, difficult to provide, expensive to measure Accuracy of the distance information

High accuracy: difficult to achieve To obtain accuracy within a factor of 2

Contents


Alternative Architectures and Related Work SPAND, Remos: provide only distance

information between hosts close to a distance server and remote hosts on the internet For each server: scales proportionally to the

number of destination For all sites in the Internet: N2

Stemm: passive monitoring Not perturb actual internet traffic Only measure regions previous traversed Not adapt to the internet topology changes More human efforts

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IDMaps Architecture

Address three questions What form does the distance

information take? What are IDMaps’ components? How should the distance information

be disseminated?

Various forms of distance information

Forms Scale commentsGlobal IP addr. H2

H: # of hostsInfeasible

Addr. Prefix(AP)

P2

P: # of APs; 200,000Easily terabytes

AS A2+P’ ( A<<P )A: # of AS, P’:# of BGP-advertised IP addr. Blocks

A = 100,000 (large)Its accuracy is highly suspected

Cluster of APs B2+PB: # of Traces

If B = 500, manageableReasonable accuracy

1

2

3

4

1

2

3

4

The form used There are three main components

APs, Tracers, and the virtual links(the raw distance)

AP: a consecutive address range of IP addresses Tracers: Some systems that are distributed around

the Internet Assumption

We can estimate the distance between two points as the sum of distances between intermediate points

AP1

AP2

Tracer1

b

ac

|a-c|<|b|<|a+c| ? Feasible to estimate

distance?

-- APs-- Tracers

An assumption: Triangulation

To support the triangulation

Set up 2 experiments: D1(1995), D2(1997)

Fig. Shows the ratios of for all shortest-path triangulation in the data sets Between 75% an 90% of triangulation

estimates fall within a factor of 2 of the real distance

The resulting estimates are acceptable!

ba

c

Tracer placement Two problems

How many tracers are optimal? Given the number of tracers, how to put to

minimize the maximum distance between an AP and the nearest tracer?

Two graph theoretic approaches that can apply K-HST algorithm Minimum K-center algorithm These algorithms are used to determine the

placement of fire stations, ambulance placement, etc. with a priori

k-HST: decide # of tracers 1st phase: The graph is recursively

partitioned: A node is arbitrarily selected from the

current(parent) partition, and all the nodes that are within a random radius from this node form a new node partition

The radius of the child partition is a factor of k smaller than the diameter of the parent partition

Recurs until each node is in a partition of its own

k-HST tree

2nd phase: virtual node is assigned to each of the partition on each level

The diameter of a partition The furthest distance between two

nodes in the partition Equals to 2 times of the length of the

links from a virtual node to its children

Use K-HST tree Devise a greedy algorithm to find the

number of tracers when the maximum distance is bounded to D

Push the tracers down the tree until it discovers a partition with diameter <=D

The number of partitions is the minimum number of tracers

Set the virtual nodes of these partitions to be the tracer

Minimum K-Center Algorithm K-Center problem

The placement of a given number of centers such that the maximum distance from a node to the nearest center is minimized

NP-complete Willing to tolerate inaccuracies within a

factor of 2(2-approximation) No worse than twice the maximum

Observation: Guarantee that the distance from a node to the nearest center is bounded

Minimum K-Center Algorithm: details

G=(V,E), E=V×V, c(e) is the cost of the shortest path between (v1, v2)

All the graph edges are arranged in non-decreasing order by cost

Gi2 is the graph whenever there is a path between

u and v in Gi of at most two hops, uv An independent set of a graph G(V,E) is such that,

for all u,vV’, the edge (u,v) is not in E An independent set of Gi

2 is thus a set of nodes in Gi that are at least 3 hops apart in Gi

The maximal independent set M as an independent set V’ such that all nodes in V-V’ are at most one hop away from nodes in V’

1. Construct Gi2,G2

2,…, Gm2

2. Compute Mi for each Gi2

3. Find the smallest I such that |Mi|<=K, say j4. Mj is the set of K centers

Algorithm 2 (2-approximate minimum-center [18]):details

Tracer Heuristics Stub-AS

only connected to one other AS Transit-AS

connected to one or more other AS allows itself to be used as a conduit for

traffic (transit traffic) between other AS's Most large ISPs are Transit-AS’s

Mixed Randomly, with uniform distribution placed

on the network

Virtual links

Tracer-tracer virtual links Not necessary to list all B2 tracer-tracer

distances Given a number of tracers in Seattle and

Boston It would almost certainly not to be useful

to know all of the distance between them Allow a sufficient distance approximation

between hosts in Seattle and hosts in Boston

Virtual links Tracer-AP VLs

A dedicated tracer? More than one

tracer?

C in AP1 will be directed to mirror M1 in AP3 instead of M2 in AP2

Had tracer T2 also traced to AP1, the client would have been directed to M2

Contents


Performance Evaluation

Topology Generation Waxman, Tiers, Inet

Simulating IDMaps Infrastructure Tracer placement: Stub-AS, Transit-AS

Distance map computation Tracer-tracer VLs and Tracer-AP VLs

Performance Metric Computation

Nearest mirror selection Papp: the percentage of correct IDMaps’

answers over total number of clients Consider IDMaps’ server selection

correct As long as the distance between a client

and the nearest mirror determined by IDMaps is within a factor of λ times the distance between the client and the actual nearest mirror ( we use λ=2)

Simulation result Mirror selection using IDMaps gives

noticeable improvement over random selection

Network topology can affect IDMaps’ performance

Tracer placement heuristics that do not rely on network topology can perform as well or better than algorithms that requires a priori knowledge of the topology

Simulation result Adding more tracers gives

diminishing return Number of tracer-tracer VLs required

for good performance can be on the order of B with a small constant

Increasing the number of tracers tracing to each AP improves IDMaps’ performance with diminishing return

Mirror selection Transit-AS

The probability of that at least 80% of all clients will be directed to the “correct” mirror is 100%

Up to 98% of all clients will be directed to the correct mirror is only 85%

Mirror selection

Mirror selection using distance maps outperforms random selection regardless of the tracer placement algorithm

Qualitatively, the results from agree with the conclusion: mirror selection using distance maps

outperforms random selection

Effect of Topology

Effect of Topology

Performance on Tiers generated topology exhibit a qualitatively different behavior than those on other topologies

The transit-AS heuristic gives better IDMaps performance than the k-HST algorithm on topologies generated from Inet and Waxman, but not so in the topologies generated from Tiers

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Conclusion A global distance measurement

infrastructure called IDMaps is purposed It can be placed on the Internet to collect

distance information Nearest mirror selection fro clients

Significant improvement over random selection

Do not require a full knowledge of the underling topology

Conclusion IDMaps overhead can be minimized by

grouping Internet addresses into APs to reduce the number of measurements Apply t-spanner to tracer-tracer VLs can

result in linear measurement overhead with respect to the number of tracers in the common case

Overall, this study has provided positive results to demonstrate that a useful Internet distance map service can indeed be built scalably

(Stub AS)

idmaps: a global internet host distance estimation service p. francis, s. jamin, c. jin, y. jin, d....

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