Multicast Mobility in Mobile IP Version 6 (MIPv6) : Problem Statement and Brief Survey

Publisher PD

Hierarchical Up/Down Routing Architecture for Ethernet backbones and campus networks

We describe a new layer two distributed and scalable routing architecture. It uses an automatic hierarchical node identifier assignment mechanism associated to the rapid spanning tree protocol. Enhanced up/down mechanisms are used to prohibit some turns at nodes to break cycles, instead of blocking links like the spannning tree protocol does. The protocol performance is similar or better than other turn prohibition algorithms recently proposed with lower complexity O(Nd) and better scalability. Simulations show that the fraction of prohibited turns over random networks is less than 0.2. The effect of root bridge election on the performance of the protocol is limited both in the random and regular networks studied. The use of hierarchical, tree-descriptive addresses simplifies the routing, and avoids the need of all nodes having a global knowleddge of the network topology. Routing frames through the hierarchical tree at very high speed is possible by progressive decoding of frame destination address, without routing tables or port address learning. Coexistence with standard bridges is achieved using combined devices: bridges that forward the frames having global destination MAC addresses as standard bridges and frames with local MAC frames with the proposed protocol.Publicad

Labeling Schemes with Queries

We study the question of ``how robust are the known lower bounds of labeling schemes when one increases the number of consulted labels''. Let $f$ be a function on pairs of vertices. An $f$-labeling scheme for a family of graphs \cF labels the vertices of all graphs in \cF such that for every graph G\in\cF and every two vertices $u,v\in G$, the value $f(u,v)$ can be inferred by merely inspecting the labels of $u$ and $v$. This paper introduces a natural generalization: the notion of $f$-labeling schemes with queries, in which the value $f(u,v)$ can be inferred by inspecting not only the labels of $u$ and $v$ but possibly the labels of some additional vertices. We show that inspecting the label of a single additional vertex (one {\em query}) enables us to reduce the label size of many labeling schemes significantly

Fast Routing Table Construction Using Small Messages

We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of the graph when all edges are considered to have unit weight. Given 0 < eps <= 1/2, our algorithm runs in weak-O(n^(1/2 + eps) + HD) communication rounds using messages of O(log n) bits and guarantees a stretch of O(eps^(-1) log eps^(-1)) with high probability. This is the first distributed algorithm approximating weighted shortest paths that uses small messages and runs in weak-o(n) time (in graphs where HD in weak-o(n)). The time complexity nearly matches the lower bounds of weak-Omega(sqrt(n) + HD) in the small-messages model that hold for stateless routing (where routing decisions do not depend on the traversed path) as well as approximation of the weigthed diameter. Our scheme replaces the original identifiers of the nodes by labels of size O(log eps^(-1) log n). We show that no algorithm that keeps the original identifiers and runs for weak-o(n) rounds can achieve a polylogarithmic approximation ratio. Variations of our techniques yield a number of fast distributed approximation algorithms solving related problems using small messages. Specifically, we present algorithms that run in weak-O(n^(1/2 + eps) + HD) rounds for a given 0 < eps <= 1/2, and solve, with high probability, the following problems: - O(eps^(-1))-approximation for the Generalized Steiner Forest (the running time in this case has an additive weak-O(t^(1 + 2eps)) term, where t is the number of terminals); - O(eps^(-2))-approximation of weighted distances, using node labels of size O(eps^(-1) log n) and weak-O(n^(eps)) bits of memory per node; - O(eps^(-1))-approximation of the weighted diameter; - O(eps^(-3))-approximate shortest paths using the labels 1,...,n.Comment: 40 pages, 2 figures, extended abstract submitted to STOC'1

Shortest Path versus Multi-Hub Routing in Networks with Uncertain Demand

We study a class of robust network design problems motivated by the need to scale core networks to meet increasingly dynamic capacity demands. Past work has focused on designing the network to support all hose matrices (all matrices not exceeding marginal bounds at the nodes). This model may be too conservative if additional information on traffic patterns is available. Another extreme is the fixed demand model, where one designs the network to support peak point-to-point demands. We introduce a capped hose model to explore a broader range of traffic matrices which includes the above two as special cases. It is known that optimal designs for the hose model are always determined by single-hub routing, and for the fixed- demand model are based on shortest-path routing. We shed light on the wider space of capped hose matrices in order to see which traffic models are more shortest path-like as opposed to hub-like. To address the space in between, we use hierarchical multi-hub routing templates, a generalization of hub and tree routing. In particular, we show that by adding peak capacities into the hose model, the single-hub tree-routing template is no longer cost-effective. This initiates the study of a class of robust network design (RND) problems restricted to these templates. Our empirical analysis is based on a heuristic for this new hierarchical RND problem. We also propose that it is possible to define a routing indicator that accounts for the strengths of the marginals and peak demands and use this information to choose the appropriate routing template. We benchmark our approach against other well-known routing templates, using representative carrier networks and a variety of different capped hose traffic demands, parameterized by the relative importance of their marginals as opposed to their point-to-point peak demands