Aggregated Multicast — A Comparative Study

Though IP multicast is resource ef£cient in delivering data to a group of members simultaneously, it suffers from scalability problem with the number of concurrently active multicast groups because it requires a router to keep forwarding state for every multicast tree passing through it. To solve this state scalability problem, we proposed a scheme, called aggregated multicast. The key idea is that multiple groups are forced to share a single delivery tree. In our earlier work, we introduced the basic concept of aggregated multicast and presented some initial results to show that multicast state can be reduced. In this paper, we develop a more quantitative assessment of the cost/bene£t trade-offs. We propose an algorithm to assign multicast groups to delivery trees with controllable cost and introduce metrics to measure multicast state and tree management overhead for multicast schemes. We then compare aggregated multicast with conventional multicast schemes, such as source speci£c tree scheme and shared tree scheme. Our extensive simulations show that aggregated multicast can achieve signi£cant routing state and tree management overhead reduction while containing the expense of extra resources (bandwidth waste and tunnelling overhead). We conclude that aggregated multicast is a very cost-effective and promising direction for scalable transit domain multicast provisioning.

Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.