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The implementation of network services is changed from dedicated hardware to software middleboxes with the evolution of Network Function Virtualization (NFV). The placement of such middleboxes are complicated not only by the selection of multiple available hosting servers, but also by the traffic-changing effect of middleboxes. In this paper, we address the placement problem of a single type of traffic-diminishing middlebox (e.g., spam filters), where the objective is to minimize the total bandwidth consumption when the total number of placed middleboxes is limited. We prove the NP-hardness of checking the feasibility of our problem in general topologies. Then we propose a greedy solution and prove that it is performance-guaranteed when it generates a feasible deployment. Next we narrow down to tree-structured networks and propose an optimal dynamic programming based strategy. In order to improve the time efficiency, we also introduce an efficient greedy solution with an intuitive insight. Extensive simulations are conducted on a real-world dataset to evaluate the performance of our algorithms.

Optimizing Flow Bandwidth Consumption with Traffic-diminishing Middlebox Placement