We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all nodes in an arbitrary weighted undirected network. This answers an open question of Gavoille and Gengler who showed that any universal compact routing algorithm with maximum stretch strictly less than 3 must use\Omega\Gamma n) local space at some vertex. 1 Introduction Let G = (V; E) with jV j = n be a labeled undirected network. Assuming that a positive cost, or distance is assigned with each edge, the stretch of path p(u; v) from node u to node v is defined as jp(u;v)j jd(u;v)j , where jd(u; v)j is the length of the shortest u \Gamma v path. The approximate all-pairs shortest path problem involves a tradeoff of stretch against time-- short paths with stretch bounded by a constant are com...

this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. This article is not intended to be a comprehensive survey on ad hoc networking. The choice of the problems discussed in this article are somewhat biased by the research interests of the author

This paper is concerned with compact routing schemes for arbitrary undirected networks in the name-independent model first introduced by Awerbuch, Bar-Noy, Linial and Peleg. A compact routing scheme that uses local routing tables of size Õ(n1/2), 1 O(log 2 n)-sized packet headers, and stretch bounded by 5 is obtained, where n is the number of nodes in the network. Alternative schemes reduce the packet header size to O(log n) at the cost of either increasing the stretch to 7 or increasing the table size to Õ(n2/3). For smaller table-size requirements, the ideas in these schemes are generalized to a scheme that uses O(log 2 n)-sized headers, Õ(k2 n 2/k)-sized tables, and achieves a stretch of min{1 + (k − 1)(2 k/2 − 2), 16k 2 − 8k}, improving the best previously-known name-independent scheme due to Awerbuch and Peleg. 1

This paper introduces the first near-linear (specifically, O(E log n + n log 2 n)) time algorithm for constructing a sparse neighborhood cover in sequential and distributed environments. This automatically implies analogous improvements (from quadratic to near-linear) to all the results in the literature that rely on network decompositions, both in sequential and distributed domains, including adaptive routing schemes with ~ O (1) 1 stretch and memory, small edge cuts in planar graphs, sequential algorithms for dynamic approximate shortest paths with ~ O (E) cost for edge insertion/deletion and ~ O (1) time to answer shortest-path queries, weight and distance-preserving graph spanners with ~ O (E) running time and space, and distributed asynchronous "from-scratch" Breadth-First-Search and network synchronizer constructions with ~ O (1) message and space overhead (down from O(n)). Lab. for Computer Science, MIT, Cambridge, MA 02139. Supported by Air Force Contract AFOSR F4962092 ...

1 ) Baruch Awerbuch David Peleg y Abstract: This abstract presents a collection of clustering and decomposition techniques enabling the construction of sparse and locality preserving representations for arbitrary networks. These new clustering techniques have already found several powerful applications in the area of distributed network algorithms. Two of these applications are described in this abstract, namely, routing with polynomial communication-space tradeoff and online tracking of mobile users. 1 Introduction 1.1 Motivation As networks grow larger, various control and management functions become increasingly more complex and expensive. Traditional protocols, based on a global approach, require all sites to participate in their activities, and to maintain considerable amounts of global information (e.g. topological data, status tables etc). This becomes problematic due to space considerations, the complexity of maintaining and updating this global information and the incre...

Consider an arbitrary distributed network in which large numbers of objects are continuously being created, replicated, and destroyed. A basic problem arising in such an environment is that of organizing a distributed directory service for locating object copies. In this paper, we present a new data tracking scheme for locating nearby copies of objects in arbitrary distributed environments. Our tracking scheme supports ecient accesses to data objects while keeping the local memory overhead low. In particular, our tracking scheme achieves an expected polylog(n)- approximation in the cost of any access operation, for an arbitrary network. The memory overhead incurred by our scheme is O(polylog(n)) times the maximum number of objects stored at any node, with high probability. We also show that our tracking scheme adapts well to dynamic changes in the network. 1 College of Computer Science, Northeastern University, Boston, MA 02115, rraj@ccs.neu.edu. Supported by NSF CAREER award NSF CCR{9983901. 2 Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85287-5406, aricha@asu.edu. Supported in part by NSF CAREER Award CCR{9985284 and NSF Grant CCR{9900304. 3 Max-Planck-Institut f ur Informatik, Saarbr ucken, Germany. Supported in part by the IST Programme of the EU under contrac number IST-1999-14186 (ALCOM-FT) 4 Compaq Corporation, San Jose, CA, Gayathri.Vuppuluri@compaq.com. This work was done while the author was a graduate student at Arizona State University, supported in part by NSF CAREER Award CCR{9985284. 1

Abstrucf- This note deals with store-and-forward deadlock prevention in communication networks. The approach we adopt is that of establishing buffer classes in order to prevent cyclic waiting chains. This type of solutions usually tends to require many buffers. The main contribution of the current note is in showing that the number of required buffers can be reduced considerably by employing a hierarchical organization of the network. The note proposes a new hierarchical scheme for arbitrary networks, that features a tradeoff between the communication overhead and the buffer requirements of the routing. This tradeoff can be shown to be close to optimal. 0 I.

The first sublinear space universal compact routing schemes for directed graphs are presented. The first scheme uses O( p n log 2 n)-sized routing tables on average at each node, and the second achieves O(n 2=3 log 4=3 n)-sized routing tables maximum space at every node. Both schemes use O(logn) bit vertex addresses and achieve roundtrip routes of stretch at most 3 compared to the optimal roundtrip shortest paths in any strongly connected weighted or unweighted digraph. 1 Introduction The approximate shortest path problem is concerned with computing short routes between pairs of nodes in a network faster than the time it would take to find the shortest paths exactly, although the length of the route may be longer that the shortest path between the nodes. The compact routing problem instead considers a tradeoff of route lengths for space, in the setting where each node locally stores its own routing tables. Much recent work has been done on fast constructions of approximate sh...