Ageev A.A., Baburin A.E., Gimandi E.K.'s A 3/4-Approximation Algorithm for Multiple Subset Sum PDF

By Ageev A.A., Baburin A.E., Gimandi E.K.

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Suppose without lose of generality that the selected nodes are r2 and r4. Let us turn to describe the different SPTs of the nodes in G ( V , E ). The SPTs and are very similar. The SPT contains the edge (r2, r3) and all the incident edges of node r1 except edge (r1, r3). The SPT contains the edge (r4, r5) and all the incident edges of node r1 except edge (r1, r5). These two SPTs together guarantee that any shortest path that one of its end-node is in the set R is covered. They also cover the shortest path between every pair of nodes u, v ∈ V such that (u, v) ∉ E.

23], reformulate the monitoring placement problem. They assume that every node may be a monitoring station at any given time and then they ask the question which monitors should be activated and what should be their sampling to achieve a given measurement task? To this problem they provide optimal solution. 3. Network model We model the Service Provider or Enterprise IP network by an undirected graph G(V,E), where the graph nodes, V, denote the network routers and the edges, E, represent the communication links connecting them.

Recall that by sending a single probe from r1 to every other node We can calculate the path delay of every path that traverses through node r2 and every sub-paths of these paths. This requires 2·│ │+1 probes assign to r1. Thus the only paths that are not monitored by r2 are the ones that contain an edge (wi,wj ), corresponding to edges ( , ) in . These include the paths = {ui,wi,,wj , uj}, = {wi,wj , uj}, = {ui,wi,wj} and = {wi,wj}. Consider such path = {ui,wi,wj , uj}. This path can be monitored only by ui or uj .

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A 3/4-Approximation Algorithm for Multiple Subset Sum by Ageev A.A., Baburin A.E., Gimandi E.K.


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