On the Complexity of the Regenerator Placement Problem in Optical Networks

Abstract

Placement of regenerators in optical networks has attracted the attention of recent research works in optical networks. In this problem, we are given a network with an underlying topology of a graph G and with a set of requests that correspond to paths in G There is a need to put a regenerator every certain distance, because of a decrease in the power of the signal. In this paper, we investigate the problem of minimizing the number of locations to place the regenerators. We present analytical results regarding the complexity of this problem, in four cases, depending on whether or not there is a bound on the number of regenerators at each node, and depending on whether or not the routing is given or only the requests are given (and part of the solution is also to determine the actual routing). These results include polynomial time algorithms, NP-completeness results, approximation algorithms, and inapproximability results

Predeployment of Transponders for Dynamic Lightpath Provisioning in Translucent Spectrally–Spatially Flexible Optical Networks

“…The authors of Reference [13] showed that the RLP is NP-Complete and developed three heuristics for the RLP based on various graph theory approaches. In Reference [16], analytical results showing the complexity of the RPL problem were presented. Four cases were considered with an upper bound on the number of regenerators installed at each node and where information on routing and/or information on the requests were given.…”

Regenerator pool site selection for mixed line rate optical networks

“…In [6], it is proved that the regenerator pool sites selection problem in single line rate optical network is NP-complete. Since this problem is a special case of our problem when only a single line rate is available, our problem is also NPcomplete.…”

“…In [6], an approximation algorithm is proposed for the regenerator pool site selection problem in single line rate optical networks (SLR-RPSS). As this algorithm will be used as a sub-routine in our heuristic approaches, it is necessary to describe the algorithm in this paper.…”

“…When the network load increases, the average number of regenerator pool sites obtained by the Sequential HLRF, Sequential LLRF, MLR-combined, and Weighted MLR-combined algorithms approaches around 8. The 8 nodes that are most likely to be chosen as regenerator pool sites are Nodes 1,2,4,6,7,9,11,and 14, as shown in black in Fig. 2.…”

“…In [6], the regenerator site selection problem is considered under four scenarios, depending on whether or not routing is given with the request, and whether or not there is a limit on the number of regenerators at each node. Our work differs from this work in that we consider mixed line rate signals with different reachabilities, which makes the problem more complex.…”