Barbara Simons

Fault-tolerant clock synchronization

This paper gives two simple efficient distributed algorithms: one for keeping clocks in a network synchronized and one for allowing new processors to join the network with their clocks synchronized. The algorithms tolerate both link and node failures of any type. The algorithm for maintaining synchronization will work for arbitrary networks (rather than just completely connected networks) and tolerates any number of processor or communication link faults as long as the correct processors remain connected by fault-free paths. It thus represents an improvement over other clock synchronization algorithms such as [LM1,LM2,LL1]. Our algorithm for allowing new processors to join requires that more than half the processors be correct, a requirement which is provably necessary.

Scheduling Unit–Time Tasks with Arbitrary Release Times and Deadlines

The basic problem considered is that of scheduling n unit-time tasks, with arbitrary release times and deadlines, so as to minimize the maximum task completion time. Previous work has shown that this problem can be solved rather easily when all release times are integers. We are concerned with the general case in which noninteger release times are allowed, a generalization that considerably increases the difficulty of the problem even for only a single processor. Our results are for the one-processor case, where we provide an

An Overview of Clock Synchronization

O(n\log n)

A new look at fault-tolerant network routing

algorithm based on the concept of “forbidden regions”.

Multiprocessor Scheduling of Unit-Time Jobs with Arbitrary Release Times and Deadlines

A distributed system consists of a set of processors that communicate by message transmission and that do not have access to a central clock. Nonetheless, it is frequently necessary for the processors to obtain some common notion of time, where ~time :~ can mean either an approximation to real time or simply an integer-valued counter. The technique that is used to coordinate the notion of time is known as clock synchronization.

A fast algorithm for single processor scheduling

Abstract We model a communication network as a graph in which a processor is a node and a communication link is an edge. A routing for such a network is a fixed path, or route, between each pair of nodes. Given a network with a predefined routing, we study the effects of faulty components on the routing. Of particular interest is the number of routes along which a message must travel between any two non-faulty nodes. This problem is analyzed for specific families of graphs and for classes of routings. We also give some bounds for general versions of the problem. Finally, we conclude with one of the most important contributions of this paper, a list of interesting and apparently difficult open problems.

Dynamic fault-tolerant clock synchronization

We present a polynomial time algorithm for constructing an optimal schedule, if a feasible schedule exists, for tthe following multimachine scheduling problem. There are n unit-time jobs, with arbitrary release times and deadlines, and m identical parallel machines. A feasible schedule is one in which no job is started before it is released, each job is completed by its deadline, and no job is interrupted once it begins to run.

A fast algorithm for multiprocessor scheduling of unit-length jobs

Suppose we are given a single processor and a set S of n jobs. For each job X there is a release time rx and a deadline dx , with rx and dx nonnegative real numbers. A schedule is feasible if there is no time at which more than one job is being run and if every job in the schedule is begun no earlier than its release time and is completed by its deadline. The problem is to find a feasible schedule in which each job is run for the same amount of time p. The processing is nonpreemptive in that once a job is started it continues executing until it has run for precisely p units of time.

Optimizations for Efficient Array Redistribution on Distributed Memory Multicomputers

This paper gives two simple efficient distributed algorithms: one for keeping clocks in a network synchronized and one for allowing new processors to join the network with their clocks synchronized. Assuming a fault-tolerant authentication protocol, the algorithms tolerate both link and processor failures of any type. The algorithm for maintaining synchronization works for arbitrary networks (rather than just completely connected networks) and tolerates any number of processor or communication link faults as long as the correct processors remain connected by fault-free paths. It thus represents an improvement over other clock synchronization algorithms such as those of Lamport and Melliar Smith and Welch and Lynch, although, unlike them, it does require an authentication protocol to handle Byzantine faults. Our algorithm for allowing new processors to join requires that more than half the processors be correct, a requirement that is provably necessary.

Parallel Program Graphs and their Classification

An efficient polynomial time algorithm for the problem of scheduling n unit length jobs with rational release times and deadlines on m identical parallel machines is presented. By using preprocessing, a running time of