1. Locating network monitors: complexity, heuristics, and coverage Kyoungwon Suh Yang Guo Jim Kurose Don Towsley

2. Motivation Need to understand the performance of the network infrastructure. A monitor can achieve this goal. –A monitor is placed inside a router –A monitor can be deployed as a standalone measure box that taps into a communication link A monitor may capture or sample packets carried by this link In order to capture large fraction of the traffic, we may place multiple monitors on different links.

3. Several things we need to consider when deploying the monitors. –Placing a monitor on a link incurs a deployment cost: Hardware/software cost Space cost Maintenance cost –Each operation by the monitor also incurs some cost. Per-packet operating cost –Placing the monitors on different position may have different benefits. The general goal will be maximizing the benefit while minimizing the cost.

4. Problem setting A flow: a collection of packets going through the same route on the network. D: a set of all flows. S i : the set of all flows carried by link i. y i : whether a monitor is deployed at link i. –y i = 1: deployed. –y i = 0: not deployed.

5. Deployment cost: deployment cost may be different from link to link. –f i : the cost of deploying a monitor on link i. –The total deployment cost is: Operating cost: –Depend on the link speed, specific to the link, c i: the cost per-packet at link i. –Depend on the volume of flows the monitor is monitoring  j : the number of packets sent by flow j. m ij : the fraction of flows sampled by the monitor on link i. –The total operating cost:

6. Monitoring reward: –The reward depends on which flow is monitored. –The reward depends on what fraction of each flow is monitored If the monitor can capture every packet traversing the link, If the monitor only sample a fraction of each flow

7. Monitoring problems without sampling Each monitor collects all the packets of monitored flows, –m ij = 1 or 0 for all i, j. Budget Constrained Maximum Coverage problem (BCMCP) –Total deployment cost is constrained. –Maximize benefit –Operating cost is ignored Minimum deployment cost problem (MDCP) –A certain amount of monitoring reward should be guaranteed –Minimize the deployment cost –Operating cost is ignored Minimum deployment and operating cost problem (MDOCP) –Minimize the sum of deployment and operating cost

8. Budget Constrained Maximum Coverage problem (BCMCP) Problem formulation The problem is NP-Complete, which can be shown by a reduction from a known NP-Complete problem, budgeted maximum coverage problem (MCP).

9. Budgeted maximum coverage problem (MCP) Definition: –A collection of sets S = { S 1, S 2, …, S m } with associated costs {c 1, c 2, …, c m } over a a domain of elements X = {x 1, x 2, …, x n }with associated weights {w 1, w 2, …, w n } – Goal: find sets S’  S such that total cost of elements in S’ does not exceed a given budget L and the total weight of elements covered by S’ is maximized. This problem is known to be NP-Complete Find some approximation algorithm –Performance of an approximation algorithm A. A is said to achieve approximation ratio  if the weight generated by A is at least (  * optimal)