An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the smallest number of colors that are required in order to make G conflict-free connected. A coloring of vertices of a hypergraph H = (...

Non –crossing set partitions are counted by the Catalan numbers and have been extensively studied in mathematics. We introduce the concept of a non-crossing tree partition and then use generating functions to count the number non-crossing tree partitions in Ordered and Binary Phylogenetic trees. In addition, we explore the connection between convexity, tree partitions and independent sets. Last...

We describe three new Jacobi orderings for parallel computation of SVD problems on tree architectures. The rst ordering uses the high bandwidth of a perfect binary fat-tree to minimise global interprocessor communication costs. The second is a new ring ordering which may be implemented e ciently on an ordinary binary tree. By combining these two orderings, an e cient new ordering, well suited f...

In order to offer multimedia services to the user, a powerful signaling system for broadband networks is required. Our work aims at an overall signaling architecture with totally independent call and connection control. This paper focusses on MCMP (multicast connection management protocol), a connection control solution that can be used in this context. MCMP offers a uniform interface to the te...

The technique of Virtual Paths is used in ATM networks to perform bandwidth allocation for virtual circuits and to simplify setting up of virtual circuits in response to connection requests. In this paper, we describe a new technique called Virtual Trees that can be used for bandwidth allocation in ATM networks. A Virtual Tree corresponds to pre-allocated bandwidth along a set of links in the n...

Data analysis on non-Euclidean spaces, such as tree spaces, can be challenging. The main contribution of this paper is establishment of a connection between tree data spaces and the well developed area of Functional Data Analysis (FDA), where the data objects are curves. This connection comes through two tree representation approaches, the Dyck path representation and the branch length represen...

This note introduces a new coding method for binary trees in which the code item corresponding to a node equals node's distance from the left arm of the tree according to the metrics defined by the tree. The new coding method is compared with previously known methods. Moreover, we establish a connection between distance-based methods and a recently introduced method by Johnsen.

The shallow water equations in Cartesian coordinates and two dimensions are solved on the Connection Machine 2 (CM-2) using both the spectral and finite difference methods. A description of these implementations is presented together with a brief discussion of the CM-2 as it relates to these specific computations. The finite difference code was written both in C* and *LISP and the spectral code...

In this paper, we present new methods for load balancing of unstructured tree computations on large-scale SIMD machines, and analyze the scalability of these and other existing schemes. An e cient formulation of tree search on a SIMD machine comprises of two major components: (i) a triggering mechanism, which determines when the search space redistribution must occur to balance search space ove...