On Conflict-Free All-to-All Broadcast in One-Hop Optical Networks of Arbitrary Topologies

In this paper, we investigate the problem of all-to-all broadcast in optical networks, also known as gossiping. This problem is very important in the context of control plane design as it relates to status information dissemination. We present a routing and wavelength assignment (RWA) method to reduce the number of wavelengths such that the communication is conflict-free in a wavelength division multiplexing (WDM) optical environment without wavelength converters. Our approach utilizes the tap-and-continue capability of the optical nodes. The network topology is considered to be arbitrary as long as it is connected. Both cases of maximally and nonmaximally edge-connected graphs are studied. For the first case, we give a closed-form expression for the lower bound on the number of wavelengths, which is an elegant extension of the results in for concurrent broadcast trees in optical networks. Furthermore, we show how to achieve this bound. The second case is more involved and requires a specific procedure to achieve the minimum number of wavelengths. For this case, we provide an attractive method for the RWA algorithm that attempts to minimize the number of wavelengths. Our solution for this case is within a constant factor that is strictly less than 2 from the optimal solution. The proposed algorithm uses the concept of "cactus" representation of all minimum edge-cuts in a graph in a novel recursive approach.