Sub-Tree-Based Approach for Reconfiguration of Light-Tree Pair without Flow Interruption in Sparse Wavelength Converter Network

Network reconfiguration is an important mechanism for network operators to optimize network performance and optical flow transfer. It concerns unicast and multicast connections. Multicast connections are required to meet the bandwidth requirements of multicast applications, such as Internet Protocol-based TeleVision (IPTV), distance learning, and telemedicine. In optical networks, a multicast connection is made possible by the creation of an optical tree-shaped path called a light-tree. The problem of light-tree pair reconfiguration is addressed in this study. Given an initial light-tree used to transfer an optical flow and a final light-tree that is computed by the network operator to optimize network performance, the goal is to migrate the optical flow from the initial light-tree to the final light-tree without flow interruption. Flow interruption is not desirable for network operators because it forces them to pay financial penalties to their customers. To solve this problem, existing methods use a branch approach that is inefficient if some network nodes do not have wavelength conversion capability. Therefore, we proposed in this study a sub-tree-based method. This approach selects and configures sub-tree pairs from the light-tree pair (initial light-tree, final light-tree) to be reconfigured. Then, we produce a sequence of configurations. The performance study confirms that our method is efficient in solving the problem of light-tree pair reconfiguration because our method does not cause flow interruption.

An improved mode of running PASTA

PASTA is a method for estimating alignments and trees that has been able to provide excellent accuracy on large sequence datasets. By design, PASTA operates using iteration, in which the tree from the previous iteration is used to inform a divide-and-conquer strategy during which a new alignment is computed on the sequence dataset, and then a new maximum likelihood tree is estimated on the new alignment. In its default setting, PASTA runs for three iterations and returns that alignment/tree pair from the last iteration. Here we use both biological and simulated nucleotide datasets to show that returning the alignment/tree pair that has the best maximum likelihood score improves on the default usage.

CYCLIC SUBGROUPS ARE QUASI-ISOMETRICALLY EMBEDDED IN THE THOMPSON–STEIN GROUPS

We give criteria for determining the approximate length of elements in any given cyclic subgroup of the Thompson–Stein groups F(n1,…,nk) such that n1 - 1|ni - 1 ∀i ∈ {1,…,k} in terms of the number of leaves in the minimal tree-pair diagram representative. This leads directly to the result that cyclic subgroups are quasi-isometrically embedded in the Thompson–Stein groups. This result also leads to the corollaries that ℤn is also quasi-isometrically embedded in the Thompson–Stein groups for all n ∈ ℕ and that the Thompson–Stein groups have infinite dimensional asymptotic cone.