Baruch Awerbuch

Complexity of network synchronization

The problem of simulating a synchronous network by an asynchronous network is investigated. A new simulation technique, referred to as a synchronizer, which is a new, simple methodology for designing efficient distributed algorithms in asynchronous networks, is proposed. The synchronizer exhibits a trade-off between its communication and time complexities, which is proved to be within a constant factor of the lower bound.

An on-demand secure routing protocol resilient to byzantine failures

An ad hoc wireless network is an autonomous self-organizing system ofmobile nodes connected by wireless links where nodes not in directrange can communicate via intermediate nodes. A common technique usedin routing protocols for ad hoc wireless networks is to establish therouting paths on-demand, as opposed to continually maintaining acomplete routing table. A significant concern in routing is theability to function in the presence of byzantine failures whichinclude nodes that drop, modify, or mis-route packets in an attempt todisrupt the routing service.We propose an on-demand routing protocol for ad hoc wireless networks that provides resilience to byzantine failures caused by individual or colluding nodes. Our adaptive probing technique detects a malicious link after log n faults have occurred, where n is the length of the path. These links are then avoided by multiplicatively increasing their weights and by using an on-demand route discovery protocol that finds a least weight path to the destination.

Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems

This paper develops linear time distributed algorithms for a class of problems in an asynchronous communication network. Those problems include Minimum-Weight Spanning Tree (MST), Leader Election, counting the number of network nodes, and computing a sensitive decomposable function (e.g. majority, parity, maximum, OR, AND). The main problem considered is the problem of finding the MST. This problem, which has been known for at least 9 years, is one of the most fundamental and the most studied problems in the field of distributed network algorithms. Any algorithm for any one of the problems above requires at least &OHgr;(<italic>E</italic> + <italic>V</italic>log<italic>V</italic>) communication and &OHgr;(<italic>V</italic>) time in the general network. In this paper, we present new algorithms, which achieve those lower bounds. The best previous algorithm requires &THgr;(<italic>E</italic> + <italic>V</italic>log<italic>V</italic>) in communication and &THgr;(<italic>V</italic> log <italic>V</italic>) in time. Our result enables to improve algorithms for many other problems in distributed computing, achieving lower bounds on their communication and time complexities.

Sparse partitions

A collection of clustering and decomposition techniques that make possible the construction of sparse and locality-preserving representations for arbitrary networks is presented. The representation method considered is based on breaking the network G(V,E) into connected regions, or clusters, thus obtaining a cover for the network, i.e. a collection of clusters that covers the entire set of vertices V. Several other graph-theoretic structures that are strongly related to covers are discussed. These include sparse spanners, tree covers of graphs and the concepts of regional matchings and diameter-based separators. All of these structures can be constructed by means of one of the clustering algorithms given, and each has proved a convenient representation for handling certain network applications.<<ETX>>

Self-stabilization by local checking and correction

The first self-stabilizing end-to-end communication protocol and the most efficient known self-stabilizing network reset protocol are introduced. A simple method of local checking and correction, by which distributed protocols can be made self-stabilizing without the use of unbounded counters, is used. The self-stabilization model distinguishes between catastrophic faults that abstract arbitrary corruption of global state, and other restricted kinds of anticipated faults. It is assumed that after the execution starts there are no further catastrophic faults, but the anticipated faults may continue to occur.<<ETX>>

Network decomposition and locality in distributed computation

The authors introduce a concept of network decomposition, a partitioning of an arbitrary graph into small-diameter connected components, such that the graph created by contracting each component into a single node has low chromatic number. They present an efficient distributed algorithm for constructing such a decomposition and demonstrate its use for design of efficient distributed algorithms. The method yields new deterministic distributed algorithms for finding a maximal independent set in an arbitrary graph and for ( Delta +1)-coloring of graphs with maximum degree Delta . These algorithms run in O(n/sup epsilon /) time for epsilon =O((log log n/log n)/sup 1/2/), whereas the best previously known deterministic algorithms required Omega (n) time. The techniques can also be used to remove randomness from the previously known most distributed breadth-first search algorithm.<<ETX>>

High Throughput Route Selection in Multi-rate Ad Hoc Wireless Networks

Modern wireless devices, such as those that implement the 802.11b standard, utilize multiple transmission rates in order to accommodate a wide range of channel conditions. Traditional ad hoc routing protocols typically use minimum hop paths. These paths tend to contain long range links that have low effective throughput and reduced reliability in multi-rate networks. In this work, we present the Medium Time Metric (MTM), which is derived from a general theoretical model of the attainable throughput in multi-rate ad hoc wireless networks. MTM avoids using the long range links favored by shortest path routing in favor of shorter, higher throughput, more reliable links. We present NS2 simulations that show that using MTM yields an average total network throughput increase of 20% to 60%, depending on network density. In addition, by combining the MTM with a medium time fair MAC protocol, average total network throughput increases of 100% to 200% are obtained over traditional route selection and packet fairness techniques.

Concurrent online tracking of mobile users

This paper deals with the problem of maintaining distributed directory server, that enables us to keep track of mobile users in a distributed network in the presence of concurrent requests. The paper uses the graph-theoretic concept of regional matching for implementing efficient tracking mechanisms. The communication overhead of our tracking mechanism is within a polylogarithmic factor of the lower bound.

Atomic shared register access by asynchronous hardware

The contribution of this paper is two-fold. First, we describe two ways to construct multivalued atomic n-writer n-reader registers. The first solution uses atomic 1-writer 1-reader registers and unbounded tags. the other solution uses atomic 1-writer n-reader registers and bounded tags. The second part of the paper develops a general methodology to prove atomicity, by identifying a set of criteria which guaranty an effective construction for the required atomic mapping. We apply the method to prove atomicity of the two implementations for atomic multiwriter multireader registers.

Routing with polynomial communication-space trade-off

This paper presents a family of memory-balanced routing schemes that use relatively short paths while storing relatively little routing information. The quality of the routes provided by a scheme is measured in terms of their stretch, namely, the maximum ratio between the length of a route connecting some pair of processors and their distance. The hierarchical schemes