By Witold Bednorz
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Extra info for Advances in Greedy Algorithms
As we have shown in Theorem 5 this guarantees a solution is at most with in a factor of 2 from the optimal. □ 6. Path monitoring algorithms In this section, we address the problem of designing an accurate path monitoring system that guarantees that every routing path is monitored by a single monitoring station. First, we present the need for path monitoring and then we provide greedy algorithms for station selection and probe assignment. 1 The need for path monitoring A delay-monitoring system should be able to provide accurate estimates of the end-to-end delay of the routing paths between arbitrary nodes in the network.
Ramanathan and D. Moore. ”. In Proceedings of IEEE INFOCOM’2001, Anchorage, Alaska, April 2001. A Greedy Scheme for Designing Delay Monitoring Systems of IP Networks 37  Y. Bejerano abd R. Rastogi, “Robust monitoring of link delays and faults in IP networks”. In Proceedings of the IEEE INFOCOM’2003, San Francisco, CA, USA, April 2003.  V. Chavatel, “A Greedy Heuristic for the Set-Covering Problem”, Math. of Operation Research, Vol. 4, No. 3, pp 233-235, 1979.  K. Moore, “SONAR - A Network Proximity Service, Version 1”.
Unfortunately, both the station selection and the probe assignment problems are NP-hard. However, by using greedy approximation algorithms the scheme finds solutions close to the best possible approximations to both the station selection and the probe assignment problems. Further, the experimental results demonstrate the effectiveness of the presented algorithms for accurately monitoring large networks with very few monitoring stations and probe messages close to the number of network links. 9.