## Abstract

Light-trees can efficiently guarantee point-to-multipoint connection in optical
networks for many widely used multicast applications, such as Internet protocol
television (IPTV). The establishment of a light-tree requires the placement of
*3R regenerators* along the tree due to the *wavelength
continuity constraint* and *physical impairments*. Thus,
the problem is to establish a light-tree and to assign wavelengths such that the
number of regenerators is minimized. We call this problem the *efficient 3R
regenerator placement* (ERP) problem. If we fix the routing of the
multicast tree, then how to place a minimum number of regenerators and assign
wavelengths to links becomes a subproblem of ERP, which is named the
*wavelength assignment and regenerator placement* (WARP) problem.
We find that ERP is NP-hard, and then provide an approximation algorithm named
SPT-ReWa, which has a subroutine named ReWa which can solve WARP optimally. We prove
that ReWa can find an optimal solution for WARP, and we analyze the approximation
ratio of SPT-ReWa for ERP. Finally, we illustrate several simulation scenarios to
show the efficiency of SPT-ReWa.

©2011 Optical Society of America

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