Degree-constrained Minimum Latency Trees are APX-Hard

When transmitting data from a single source to many recipients, it is often desirable to use some recipients of the stream to re-broadcast the stream to other users. In such multicast systems each client may be used as a server, serving up to B other clients. Formally, we will take a set X of clients, along with a distance function d that specifies the latency (in the host network) between each pair of clients in X. Our goal will be to produce a directed spanning tree of X, rooted at some specified root 2 X, with out-degree bounded by B, and minimizing the sum of the latencies from root to every point in X. In addition to being motivated by current experimental algorithms work, the problem also interpolates naturally between the traveling repairman problem (when B = 1) and single source shortest paths (when B = n − 1). The former problem is APX-complete (in metric spaces) and the latter is in P. We explore the hardness of the problem for other values of B. In particular, we show that the problem remains APX-Hard at least up to B = Cpn for some universal constant C when the host space is a general semi-metric

SCOPE: Synergistic Content Distribution and Peer-to-Peer Networks

Distributing content on the Internet is an important economic, educational, social, and cultural endeavor. To this end, several existing efforts use traditional server-based content distribution networks (CDNs) to replicate and distribute Web and multimedia content of big content producers, such as news Web sites, or big businesses, such as online shopping websites, etc., to millions of Internet users. This approach places a large number of content servers at strategic locations on the Internet, incurring a very large deployment and operating cost. Therefore, it is available only to some wealthy companies/organizations. Individual users and small content publishers may rely on a more economical content dissemination approach based on recent peer-to-peer technology to distribute their own content. Nevertheless, it is the ephemeral and the limited resources nature of peer-to-peer networks that hinder a wide spread adoption of peer-to-peer technology as a reliable content distribution solution. It is, therefore, important that a new generation of cost-effective and reliable content distribution framework be proposed and investigated. Building on the successes and failures of previous content distribution approaches, the proposed research goal is to find and evaluate a Synergistic Content Distribution and Peer-to-Peer Networks (SCOPE). SCOPE leverages the reliability and the resourcefulness of traditional server-based CDNs while tapping on the economical and dynamic resources of peers

Connectivity Restrictions in Overlay Multicast

A large number of overlay multicast protocols have been developed, almost all of which assume universal connectivity between end hosts. However, in reality, this assumption is not valid with widespread use of Network Address Translators (NAT) and firewalls. The impact of NAT and firewall connectivity restrictions on overlay multicast, especially in the application-endpoint setting, has not been seriously considered. In this paper, we argue that it is critical to consider connectivity restrictions because NAT and firewall hosts make up a large fraction of the endpoints, affecting proper functionality as well as performance of overlay multicast protocols. We present several design enhancements that explicitly consider connectivity restrictions in overlay multicast and evaluate the design space and tradeoffs based on real Internet broadcasts and Internet testbed experiments