Amotz Bar-Noy

Mobile users: to update or not to update?

Tracking strategies for mobile users in wireless networks are studied. In order to save the cost of using the wireless links mobile users should not update their location whenever they cross boundaries of adjacent cells. This paper focuses on three natural strategies in which the mobile users make the decisions when and where to update: the time-based strategy, the number of movements-based strategy, and the distance-based strategy. We consider both memoryless movement patterns and movements with Markovian memory along a topology of cells arranged as a ring. We analyze the performance of each one of the three strategies under such movements, and show the performance differences between the strategies.

A lower bound for radio broadcast

A radio network is a synchronous network of processors that communicate by transmitting messages to their neighbors, where a processor receives a message in a given step if and only if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove the existence of a family of radius-2 networks on n vertices for which any broadcast schedule requires at least Omega((log n/ log log n)2) rounds of transmissions. This almost matches an upper bound of O(log2 n) rounds for networks of radius 2 proved earlier by Bar-Yehuda, Goldreich, and Itai.

A unified approach to approximating resource allocation and scheduling

We present a general framework for solving resource allocation and scheduling problems. Given a resource of fixed size, we present algorithms that approximate the maximum throughput or the minimum loss by a constant factor. Our approximation factors apply to many problems, among which are: (i) real-time scheduling of jobs on parallel machines, (ii) bandwidth allocation for sessions between two endpoints, (iii) general caching, (iv) dynamic storage allocation, and (v) bandwidth allocation on optical line and ring topologies. For some of these problems we provide the first constant factor approximation algorithm. Our algorithms are simple and efficient and are based on the local-ratio technique. We note that they can equivalently be interpreted within the primal-dual schema.

Renaming in an asynchronous environment

This paper is concerned with the solvability of the problem of processor renaming in unreliable, completely asynchronous distributed systems. Fischer et al. prove in [8] that “nontrivial consensus” cannot be attained in such systems, even when only a single, benign processor failure is possible. In contrast, this paper shows that problems of processor renaming can be solved even in the presence of up to <italic>t</italic> < <italic>n</italic>/2 faulty processors, contradicting the widely held belief that no nontrivial problem can be solved in such a system. The problems deal with <italic>renaming processors</italic> so as to reduce the size of the initial name space. When only uniqueness of the new names is required, we present a lower bound of <italic>n</italic> + 1 on the size of the new name space, and a renaming algorithm that establishes an upper bound on <italic>n</italic> + <italic>t</italic>. If the new names are required also to preserve the original order, a tight bound of 2′(<italic>n</italic> - <italic>t</italic> + 1) - 1 is obtained.

Designing broadcasting algorithms in the postal model for message-passing systems

In many distributed-memory parallel computers and high-speed communication networks, the exact structure of the underlying communication network may be ignored. These systems assume that the network creates a complete communication graph between the processors, in which passing messages is associated with communication latencies. In this paper we explore the impact of communication latencies on the design of broadcasting algorithms for fully connected message-passing systems. For this purpose, we introduce thepostal model that incorporates a communication latency parameter λ ≥ 1. This parameter measures the inverse of the ratio between the time it takes an originator of a message to send the message and the time that passes until the recipient of the message receives it. We present an optimal algorithm for broadcasting one message in systems withn processors and communication latency λ, the running time of which is Θ((λ logn)/log(λ + 1)). For broadcastingm ≥ 1 messages, we first examine several generalizations of the algorithm for broadcasting one message and then analyze a family of broadcasting algorithms based on degree-d trees. All the algorithms described in this paper are practical event-driven algorithms that preserve the order of messages.

Approximating the Throughput of Multiple Machines in Real-Time Scheduling

We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a nonpreemptive schedule that maximizes the weight of jobs that meet their respective deadlines. We give constant factor approximation algorithms for four variants of the problem, depending on the type of the machines (identical vs. unrelated) and the weight of the jobs (identical vs. arbitrary). All these variants are known to be NP-hard, and the two variants involving unrelated machines are also MAX-SNP hard. The specific results obtained are as follows: For identical job weights and unrelated machines: a greedy

Minimizing Service and Operation Costs of Periodic Scheduling

2

Shifting gears: changing algorithms on the fly to expedite Byzantine agreement

-approximation algorithm. For identical job weights and k identical machines: the same greedy algorithm achieves a tight

Tracking mobile users in wireless communications networks

\frac{(1+1/k)^k}{(1+1/k)^k-1}

Efficient routing in optical networks

approximation factor. For arbitrary job weights and a single machine: an LP formulation achieves a 2-approximation for polynomially bounded integral input and a 3-approximation for arbitrary input. For unrelated machines, the factors are 3 and 4, respectively. For arbitrary job weights and k identical machines: the LP-based algorithm applied repeatedly achieves a