Directed Steiner problems are fundamental problems in Combinatorial Optimization and Theoretical Computer Science. An important problem in this genre is the k-edge connected directed Steiner tree (k-DST) problem. In this problem, we are given a directed graph G on n vertices with edge-costs, a root vertex r, a set of h terminals T and an integer k. The goal is to find a min-cost subgraph H ⊆ G ...

Graph streams have been extensively studied, for instance, for data mining and for stream reasoning, while a fairly limited number of studies have been conducted on visualizations. Recently, edge bundling methods has been extensively investigated to reduce visual clutter in large graph visualizations, however, have focused on static graphs. This paper presents a new framework, namely StreamEB, ...

Given a degree set D = {a1 < a2 < . . . < an} of nonnegative integers, the minimum number of vertices in any tree realizing the set D is known[10]. In this paper, we study the number of vertices and multiplicity of distinct degrees as parameters of tree realizations of degree sets. We explore this in the context of both directed and undirected trees and asymmetric directed graphs (graphs which ...

Let G = (V,E) be a directed graph on n vertices and m edges. We address the problem of maintaining a depth first search (DFS) tree efficiently under insertion/deletion of edges in G. 1. We present an efficient randomized decremental algorithm for maintaining a DFS tree for a directed acyclic graph. For processing any arbitrary online sequence of edge deletions, this algorithm takes expected O(m...

The Steiner tree problem which is known to be NP-Complete is the following. Given a weighted undirected graph G = (V;E), and a set X V of terminals, the objective is to nd a tree of minimum cost which connects all the terminals. If the graph is directed, in addition to X, we are given a root r 2 V , and the objective is to nd a minimum cost arborescence which connects the root to each of the te...

This paper presents an optimal fully-dynamic recognition algorithm for directed cographs. Given the modular decomposition tree of a directed cograph G, the algorithm supports arc and vertex modification (insertion or deletion) in O(d) time where d is the number of arcs involved in the operation. Moreover, if the modified graph remains a directed cograph, the modular tree decomposition is update...

Significant interest exists within the military in moving towards an integrated services environment where traditional network services such as ftp, telnet, and e-mail can co-exist with real-time services such as voice, video, and satellite imagery. Multicast routing is an effective means of providing the efficient utilization of network resources required to realize such an environment. Tradit...

We study the asymptotic properties of a minimal spanning tree formed by n points uniformly distributed in the unit square, where the minimality is amongst all rooted spanning trees with a direction of growth. We show that the number of branches from the root of this tree, the total length of these branches, and the length of the longest branch each converge weakly. This model is related to the ...

The goal for the DIRECTED STEINER TREE problem is to find a minimum cost tree in a directed graph G = (V ,E ) that connects all terminals X to a given root r . It is well known that modulo a logarithmic factor it suffices to consider acyclic graphs where the nodes are arranged in l ≤ log |X | levels. Unfortunately the natural LP formulation has a Ω( p |X |) integrality gap already for 5 levels....

Let T be a symmetric directed tree, i.e., a tree with each edge viewed as two opposite directed links. We consider the problem of routing arbitrary sets of connection requests in T. In all-optical communication tree networks with WDM (wavelength-division multiplexing) this is equivalent to color (assign wavelengths to) a given set of directed paths so that no two directed paths of the same colo...