Given an undirected multigraph G and a subset of vertices S ` V (G), the STEINER TREE PACKING problem is to find a largest collection of edge-disjoint trees that each connects S. This problem and its generalizations have attracted considerable attention from researchers in different areas because of their wide applicability. This problem was shown to be APX-hard (no polynomial time approximation scheme unless P=NP). In fact, prior to this paper, not evenan approximation algorithm with asymptotic ratio o(n) wasknown despite several attempts. In this work, we close this huge gap by presenting the first polynomial time constant factor approximation algorithm for the STEINER TREE PACKING problem. The maintheorem is an approximate min-max relation between the maximum number of edge-disjoint trees that each connects S (i.e. S-trees) and the minimum size of an edge-cut thatdisconnects some pair of vertices in S (i.e. S-cut). Specifically, we prove that if the minimum S-cut in G has 26k edges, then G has at least k edge-disjoint S-trees; this answers Kriesell's conjecture affirmatively up to a constant multiple. The techniques that we use are purely combinatorial, where matroid theory is the underlying ground work.

Abstract- In light of the slow deployment of IP Multicast technology on the global Internet and the explosive popularity of peer-to-peer file-sharing applications, there has been a flurry of research activities investigating the feasibility of implementing multicasting capability at the application layer, referred to as Application Layer Multicasting (ALM), and numerous algorithms and protocols have been proposed. This article aims to provide researchers in the field with an understanding of ALM protocols by identifying significant characteristics, from both application requirements and networking points of view, and by using those characteristics as a basis for organizing the protocols into an integrated and well-structured format. Current trends and directions for further research are also presented. This article surveys the literature over the period 1995-2005 on different application layer multicasting approaches.

Real-time distributed multi-party/multi-stream systems are becoming more popular in many areas such as 3D tele-immersion, multi-camera conferencing and security surveillance. However, the construction of such systems in large scale is impeded by the huge demand of computing and networking resources and the lack of a simple yet powerful networking model to handle interconnection, scalability and quality of service (QoS) guarantees. We make two main contributions in the paper: (1) we propose a novel generalized ViewCast model for multiparty/multi-stream video-mediated systems that fills the gap between high-level user interest and low level per-stream management, and (2) we demonstrate the ViewCast model by applying it to the multi-party 3D Tele-Immersive (3DTI) collaboration among geographically dispersed users. More specifically, we show how the ViewCast model is used in supporting stream data dissemination, coordination and QoS management among multiple 3D tele-immersive environments. We present our experimental results in both real implementation and simulation to show that our ViewCast-based solution achieves high efficiency, scalability, and quality in supporting multi-party 3DTI collaboration.

Given an undirected graph G and a subset of vertices S ` V (G), we call the vertices in S the terminal vertices and the vertices in V (G)- S the Steiner vertices. In this thesis, we study two problems whose goals are to achieve high "connectivity " among the terminal vertices. The first problem is the Steiner Tree Packing problem, where a Steiner tree is a tree that connects the terminal vertices (Steiner vertices are optional). The goal of this problem is to find a largest collection of edge-disjoint Steiner trees. The second problem is the Steiner Rooted-Orientation problem. In this problem, there is a root vertex r among the terminal vertices. The goal is to find an orientation of all the edges in G so that the Steiner rooted-connectivity is maximized in the resulting directed graph D. Here, the Steiner rooted-connectivity is defined to be the maximum k so that the root vertex has k arc-disjoint paths to each terminal vertex in D. Both problems are generalizations of two classical graph theoretical problems: the edge-disjoint s, t-paths problem and the edge-disjoint spanning trees problem. Polynomial time algorithms and exact min-max relations are known for the classical problems. However, both problems that we study are NP-complete, and thus exact min-max relations are not expected. In the following, we say S is l-edge-connected in G if we need to remove at least l edges in order to disconnect two vertices in S. Clearly, the maximum iii l for which S is l-edge-connected in G is an upper bound on the optimal value for both problems that we study (i.e. the number of edge-disjoint Steiner trees, and the Steiner rooted-connectivity in an orientation). The main result of the Steiner Tree Packing problem is the following approximate min-max relation:

Urbana, Illinoissenting the user interest in the application layer. The design of the management framework revolves around the concept of view-aware multi-stream coordination, which leverages the central role of view semantics in 3D free-viewpoint video systems. Second, in the stream differentiation layer we present the design of view to stream mapping, where a subset of relevant streams are selected based on the relative importance of each stream to the current view. Conventional streaming controllers focus on a fixed set of streams specified by the application. Different from all the others, in our management framework the application layer only specifies the view information while the underlying controller dynamically determines the set of streams to be managed. Third, in the stream coordination layer we present two designs applicable in different situations. In the case of end-to-end 3DTI communication, a learning-based controller is embedded which provides bandwidth allocation for relevant streams. In the case of multi-party 3DTI communication, we propose a novel ViewCast protocol to coordinate the multi-stream content dissemination upon an end-system overlay network. Finally, we embed 3DTI session management in the framework which facilitates