Abstract
In the k-splittable flow problem, each commodity can only use at most k paths and the key point is to find the suitable transmitting paths for each commodity. To guarantee the efficiency of the network, minimizing congestion is important, but it is not enough, the cost consumed by the network is also needed to minimize. Most researches restrict to congestion or cost, but not the both. In this paper, we consider the bi-objective (minimize congestion, minimize cost) k-splittable problem. We propose three different heuristic algorithms for this problem, A1, A2 and A3. Each algorithm finds paths for each commodity in a feasible splittable flow, and the only difference between these algorithms is the initial feasible flow. We compare the three algorithms by testing instances, showing that choosing suitable initial feasible flow is important for obtaining good results.
Highlights
In the traditional multi-commodity flow problems, the number of paths each commodity can use is not restricted
In the multi-protocol label switched (MPLS) networks, data packets are transmitted by the label switched paths (LSPs) that support the routing of data traffic between different terminal nodes
As for the time spent on the tests of the three algorithms, it has little differences and the most time-consuming part is obtaining the initial feasible splittable flows in Step 1
Summary
In the traditional multi-commodity flow problems, the number of paths each commodity can use is not restricted. Salazar et al (2006) considered the single source k-splittable flow problem They used rounding up strategy and designed an approximation algorithm with factor (1+1/k+1/(2k-1), 1) for minimum congestion and cost under the same assumption as Kolliopoulos (2005). Jiao et al (2014) considered the minimum congestion of the single source multi-commodity flow problem in the MPLS networks and designed fast heuristic algorithms. If we only minimize the total cost, the whole demand will be transmitted on path P2 , with minimum cost 1 but maximum congestion 1 This is not a good thing for the real network with such congestion, since other commodities cannot use these edges with congestion values already 1.
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