Modern networking applications replicate data and services widely, leading to a need for location-independent routing---the ability to route queries to objects using names independent of the objects' physical locations. Two important properties of such a routing infrastructure are routing locality and rapid adaptation to arriving and departing nodes. We show how these two properties can be efficiently achieved for certain network topologies. To do this, we present a new distributed algorithm that can solve the nearest-neighbor problem for these networks. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton et al. [24].

We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extremely short. The routing decision at each node takes constant time. Yet, the stretch of these routing schemes, i.e., the worst ratio between the cost of the path on which a packet is routed and the cost of the cheapest path from source to destination, is a small constant. Our schemes achieve a near-optimal tradeoff between the size of the routing tables used and the resulting stretch. More specifically, we obtain: 1. A routing scheme that uses only ~ O(n 1=2) bits of memory at each node of an n-node network that has stretch 3. The space is optimal, up to logarithmic factors, in the sense that

This paper presents the design of a new Internet routing architecture (NIRA). In today’s Internet, users can pick their own ISPs, but once the packets have entered the network, the users have no control over the overall routes their packets take. NIRA aims at providing end users the ability to choose the sequence of Internet service providers a packet traverses. User choice fosters competition, which imposes an economic discipline on the market, and fosters innovation and the introduction of new services. This paper explores various technical problems that would have to be solved to give users the ability to choose: how a user discovers routes and whether the dynamic conditions of the routes satisfy his requirements, how to efficiently represent routes, and how to properly compensate providers if a user chooses to use them. In particular, NIRA utilizes a hierarchical provider-rooted addressing scheme so that a common type of domainlevel route can be efficiently represented by a pair of addresses. In NIRA, each user keeps track of the topology information on domains that provide transit service for him. A source retrieves the topology information of the destination on demand and combines this information with his own to discover end-to-end routes. This route discovery process ensures that each user does not need to know the complete topology of the Internet.

This article focuses on routing messages along shortest paths in tree networks, using compact distributed data structures. We mainly prove that n-node trees support routing schemes with message headers, node addresses, and local memory space of size O(log n) bits, and such that every local routing decision is taken in constant time. This improves the best known routing scheme by a factor of O(log n) in term of both memory requirements and routing time. Our routing scheme requires headers and addresses of size slightly larger than log n, motivated by an inherent trade-off between address-size and memory space, i.e., any routing scheme with addresses on log n bits requires n) bits of local memory-space. This shows that a little variation of the address size, e.g., by an additive O(log n) bits factor, has a significant impact on the local memory space.

Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete balanced binary trees is straightforward. Furthermore, for complete balanced binary trees we can easily solve the problem in a distributed way by labeling the nodes of the tree such that from the labels of two nodes alone one can compute the label of their nearest common ancestor. Whether it is possible to distribute the data structure into short labels associated with the nodes is important for several applications such as routing. Therefore, related labeling problems have received a lot of attention recently.

This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sought information involves only a small and local set of entities. In contrast, localized data representation schemes are based on breaking the information into small local pieces, or labels, selected in a way that allows one to infer information regarding a small set of entities directly from their labels, without using any additional (global) information. The survey focuses on combinatorial and algorithmic techniques, and covers complexity results on various applications, including compact localized schemes for message routing in communication networks, and adjacency and distance labeling schemes.

We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(X) at most α if every set of diameter D can be covered by 2 α sets of diameter D/2. (A doubling metric is one whose doubling dimension dim(X) is a constant.) We show how to perform (1 + τ)-stretch routing on metrics for any 0 < τ ≤ 1 with routing tables of size at most (α/τ) O(α) log 2 ∆ bits with only (α/τ) O(α) log ∆ entries, where ∆ is the diameter of the graph; hence the number of routing table entries is just τ −O(1) log ∆ for doubling metrics. These results extend and improve on those of Talwar (2004). We also give better constructions of sparse spanners for doubling metrics than those obtained from the routing tables above; for τ> 0, we give algorithms to construct (1 + τ)stretch spanners for a metric (X, d) with maximum degree at most (2 + 1/τ) O(dim(X)) , matching the results of Das et al. for Euclidean metrics.

This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems.

We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems.

Given a weighted undirected network with arbitrary node names, we present a compact routing scheme, using a O(&radic;n) space routing table at each node, and routing along paths of stretch 3, that is, at most thrice as long as the shortest paths. This is optimal in a very strong sense. It is known that no compact routing using o(n) space per node can route with stretch below 3. Also, it is known that any stretch below 5 requires &Omega;(&radic;n) space per node.