Bednorz W.'s Advances in greedy algorithms PDF

By Bednorz W.

ISBN-10: 9537619273

ISBN-13: 9789537619275

Bednorz W. Advances in grasping algorithms (In-Teh, 2008)(ISBN 9537619273)(596s)_CsAl_

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As mentioned above, at least 2·│ │+ 1 probes are required to monitors all the paths that traverse through such that A contains node r2 and any sub path of them. Now, let V’ consists of all nodes the probe (ui,wi). Since each edge (wi,wj) is in the RT of only ui or uj, A must contain one of (ui,wi) or (uj ,wj ), and thus V’ must be a vertex cover of . Further, we can show that V’ contains at most k nodes. Suppose that this is not the case and V’ contains more than k nodes. Then, A must contain more than k probes (ui,wi) for ∈ .

The edges (s2, v1) and (vi, vi+1) of every even i are assigned to station s2. In this message assignment both s1 and s2 send probe messages to every node vi and in additional s1 send probe message to s2. Hence, COST = 1 + 2·n. At the optimal assignment, A*, all the edges (vi, vi+1) are assigned to a single station either s1 or s2. Here, s1 sends messages to s2 and v1, station s2 also sends message to v1, and one message is sent to every node vi, i > 1 either from s1 or s2. Hence, COST *= 2 + n, and the limit Fig.

Since for every node v ∈ V holds that Tv ∩ E = {(v, u)│u ∈ Nv – {r1}, The set S is a solution to the instance G(V,E) of the given VC problem. 1 Lower bounds for the PM and WPM problems We now turn our attention to computing the lower bounds on the best approximations for the PM and WPM problems. In the sequel, we limit our discussion to cases where monitoring stations are selected from a given subset of nodes Y ⊆ V . In our lower bound proof, we use a polynomial reduction, , from any instance I(Z,Q) of the SC problem to a corresponding PM instance.

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Advances in greedy algorithms by Bednorz W.


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