Download PDF by Witold Bednorz: Advances in Greedy Algorithms

By Witold Bednorz

ISBN-10: 9537619273

ISBN-13: 9789537619275

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E. Crovella. “Server Selection Using Dynamic Path Characterization in Wide-Area Networks”, In Proceedings of IEEE INFOCOM'99, Kobe, Japan, April 1997. [8] K. Lai and M. Baker. “Measuring Bandwidth”. In Proceedings of IEEE INFOCOM’99, New York City, New York, March 1999. [9] C. Dovrolis, P. 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 [10] Y. Bejerano abd R. Rastogi, “Robust monitoring of link delays and faults in IP networks”.

A formal description of the algorithm is presented in Figure 3. Theorem 3 The greedy algorithm computes a ln(│V│)-approximation for the LM and WLM problems. Proof: According to [11], the greedy algorithm is a H(d)-approximation algorithm for the SC problem, where d is the size of the biggest subset and is the harmonic sequence. For the LM and WLM problems, every subset includes all the edges of the corresponding RT and its size is exactly│V│- 1. Hence, the approximation ratio of the greedy algorithm is H(│V│- 1) ≤ ln(│V│).

9. The graph Advances in Greedy Algorithms (V,E) and the RTs of the nodes. Now consider a solution of size k + 1 to the PM problem and let S = {Qj │sj ∈ }. We claim that S is a solution of size k to the given SC problem. Note that r ∈ for covering all the shortest paths between node u0 and any node ui. This is because element z0 is contained in all . Hence, S is of size k. The set sets of Q and thus edge (u0, r) is not contained in any RT – {r} covers all the shortest paths that pass through node t.

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Advances in Greedy Algorithms by Witold Bednorz


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