Cyril Gavoille

Routing in Trees

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 Ω(√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.

Compact and localized distributed data structures

Abstract.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 concentrates mainly on combinatorial and algorithmic techniques, such as adjacency and distance labeling schemes and interval schemes for routing, and covers complexity results on various applications, focusing on compact localized schemes for message routing in communication networks.

Routing in distributed networks: overview and open problems

with group communication primitives. The proceedings of the conference were published by Springer in LNCS number 1914. They were edited by Maurice Herlihy who also chaired the program committee. Most of us found time outside of the technical sessions to enjoy Toledo. Angel Alvarez was the local arrangements chair. With the help of his team from the Technical University of Madrid, he made our visit to Toledo particularly memorable. It included a evening of banqueting in Spanish style and a fine afternoon on a guided walking tour of old Toledo. The orga~zizers of DISC 2001 have a tough act to follow. But I hear they are up to the challenge. See you in Lisboa in October.

Nearest common ancestors: a survey and a new distributed algorithm

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 binary trees is straightforward. Furthermore, for complete 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.Previous optimal algorithms for nearest common ancestor queries work using some mapping from a general tree to a complete binary tree. However, it is not clear how to distribute the data structures obtained using these mappings. We conclude our survey with a new simple algorithm that labels the nodes of a rooted tree such that from the labels of two nodes alone one can compute in constant time the label of their nearest common ancestor. The labels assigned by our algorithm are of size

Routing in Networks with Low Doubling Dimension

O(\log n)

A survey on interval routing

bits where

Approximate Distance Labeling Schemes

n

Space-Efficiency for Routing Schemes of Stretch Factor Three

is the number of nodes in the tree. The algorithm runs in

Object location using path separators

O(n)

Memory requirement for routing in distributed networks

time.