Gerard Tel

Synchronous, asynchronous, and causally ordered communication

SummaryThis article studies characteristic properties of synchronous and asynchronous message communications in distributed systems. Based on the causality relation between events in computations with asynchronous communications, we characterize computations which are realizable with synchronous communications, which respect causal order, or where messages between two processes are always received in the order sent. It is shown that the corresponding computation classes form a strict hierarchy. Furthermore, an axiomatic definition of distributed computations with synchronous communications is given, and it is shown that several informal characterizations of such computations are equivalent when they are formalized appropriately. As an application, we use our results to show that the distributed termination detection algorithm by Dijkstra et al. is correct under a weaker synchrony assumption than originally stated.

Maximal matching stabilizes in quadratic time

Abstract By providing an alternative variant function, we show the time complexity of Hsu and Huangs self-stabilizing algorithm for maximal matching to be bounded by 1 2 n2 + 2n + 1 steps. We show that the new bound is almost tight by providing an execution with 1 2 n2 + n − 2 steps (if n is even).

The derivation of graph marking algorithms from distributed termination detection protocols

Abstract We show that on-the-fly garbage collection algorithms can be obtained by transforming distributed termination detection protocols. Virtually all known on-the-fly garbage collecting algorithms are obtained by applying the transformation. The approach leads to a novel and insightful derivation of, e.g., the concurrent garbage collection algorithms of Dijkstra et al. and of Hudak and Keller. The approach also leads to several new, highly parallel algorithms for concurrent garbage collection. We also analyze a garbage collecting system due to Hughes from our current perspective.

Sense of Direction in Processor Networks

We discuss recent research evaluating the benefits of certain link labellings in processor networks. Such a labelling, called Sense of Direction or SoD, allows processors to communicate more efficiently with each other, and to exploit topological properties of the network algorithmically.

Assertional Verification of a Timer Based Protocol

We introduce a timer-based protocol skeleton for end-to-end data transport and connection management. The verification of the skeleton is done using a technique of system-wide invariants. To our knowledge, this is the first time this technique is applied to timer-based distributed algorithms. The approach is extended to handle the case of inaccurate timers. Thus, the contribution of this paper is not only a rigid correctness proof of a timer-based communication protocol, but also the extension of the proof method of system-wide invariants to a wider class of distributed algorithms.

Synchronizing ABD networks

Chou et al. (1990) presented two synchronizer algorithms for ABD networks. One of their synchronizers has a round time of three, and the other has a round time of only two but requires an additional bit in every message of the simulated algorithm. The authors show that ABD synchronization can be improved by using information that can be obtained, without exchanging more messages, during the initialization of the synchronizers. The authors first contribution is a synchronizer with a round time of two that does not require an additional bit in basic messages. The second result refutes the common belief that a round time of two is the best achievable for this type of synchronizer. They show that in some network topologies a smaller round time is achievable by making the local time of simulation of the pulses dependent on the arrival time of messages received during initialization. The correctness of the synchronizers is shown by modeling this class of synchronizers as functions, and using these functions lower bounds on the round time can also be easily obtained. The authors show that their synchronizers are optimal, i.e., further reduction of the round time by the same means is not possible. >

Distributed infimum approximation

Distributed Infimum Approximation (DIA) is defined as an abstraction of several interesting problems in the field of distributed computing. Global Virtual Time approximation as well as Distributed Termination Detection are special cases of DIA, as will be argued. Three solutions to the DIA problem are given for synchronous, for bidirectional and for FIFO communication.

Bit-optimal election in synchronous rings

Abstract An election algorithm is presented for synchronous rings with unknown size. The bit complexity of the proposed algorithm is linear in the number of processes. The time complexity is polynomial in the number of processes, but exponential in the smallest identity of any process.

About the Termination Detection in the Asynchronous Message Passing Model

Starting with the works by Angluin [1] and Itai and Rodeh [11], many papers have discussed the question what functions can be computed by distributed algorithms in networks where knowledge about the network topology is limited.

Comments on "On the proof of a distributed algorithm" : always-true is not invariant

Abstract We would like to report an error in a proof given by J.-P. Verjus in [3]. More importantly, we would like to point out a difference between the notions “always-true” and “invariant”, which are identified in [3]. In his paper, Verjus claims that invariance proofs by contradiction are shorter than invariance proofs by the established method, called the “induction method” in [3]. To illustrate his idea, he proposes an alternative correctness proof for a termination detection algorithm given by Dijkstra, Feijen, and Van Gasteren [2]. We show that his—operational—proof is incorrect and incomplete (Section 1); moreover, what he shows is that a predicate is always-true, which is strictly weaker than invariance (Section 2). Instead of illustrating the merits of proofs by contradiction, the proof strongly supports our opinion that operational arguments should be avoided.