1. Distributed Network Measurements
Rohit Khandekar
IBM Watson
Joint work with
Baruch Awerbuch
JHU
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.: AAAAAAAAAA

2. Active Network Measurement Problem
Measure transmission “delays” along all links in a flow network.

3. Active Network Measurement Problem
A packet sent along a path measures the delays along that path, e.g., ping, traceroute, pathchar.

4. Active Network Measurement Problem
Packets can be sent only between certain node-pairs.
Each link should be measured enough times.
It costs (congestion) to send these packets.

5. Active Network Measurement Problem
Send minimum total flow between the pairs such that each link receives at least a unit flow.
(Send flow only along (non-simple) paths of L hops.)

6. Active Network Measurement Problem
Send minimum total flow between the pairs such that each link receives at least a unit flow.
This is a (fractional) set-cover problem with paths = sets and links = elements.
(Number of sets is huge!)

7. The Set Cover Problem Given a set of elements U
subsets S1, S2, …, Sk µ U with costs c1, c2, …, ck ¸ 0
Find
Minimum cost collection of subsets whose union is entire U.

8. The Greedy Algorithm Gives O(log n) approximation where n = |U|.
(re = 1 if e is not yet covered)
Gives O(log n) approximation where n = |U|.

9. The Fractional Greedy Algorithm
Drawback: #iterations = n/²2
Gives O(log n) ( 1 + ² ) approximation.

10. The Fractional Distributed Algorithm
Luby-Nissan (93),
Garg-Konemann (98),
Young (01)
# iterations =

11. The Active Measurement Algorithm
Associate residual requirements with the edges e:
re à exp [ — ® ·fe ]
Repeat:
Saturate all paths that (approximately) minimize the cost-to-profit ratio:
by a blocking-flow computation and update re.
e2 p re 1
log |P|
² 4
L log n
² 4
Computes (1+²) approximation in = time.

12. Thank You

13. The Fractional Set Cover Problem
The LP relaxation of the set cover IP.