Lisa Higham

Dynamic and self-stabilizing distributed matching

Finding a maximal or maximum matching in a graph is a well-understood problem for which efficient sequential algorithms exist. Applications of matchings in distributed settings make it desirable to find self-stabilizing asynchronous distributed solutions to these problems. We first present a self-stabilizing algorithm for finding a maximal matching in a general anonymous network under read/write atomicity with linear round complexity. This is followed by a self-stabilizing algorithm, with quadratic time complexity, for finding a maximum matching in a bipartite network under composite atomicity. These results represent significant progress in the area of distributed algorithms for matchings.

Specifying memory consistency of write buffer multiprocessors

Write buffering is one of many successful mechanisms that improves the performance and scalability of multiprocessors. However, it leads to more complex memory system behavior, which cannot be described using intuitive consistency models, such as Sequential Consistency. It is crucial to provide programmers with a specification of the exact behavior of such complex memories. This article presents a uniform framework for describing systems at different levels of abstraction and proving their equivalence. The framework is used to derive and prove correct simple specifications in terms of program-level instructions of the sparc total store order and partial store order memories.The framework is also used to examine the sparc relaxed memory order. We show that it is not a memory consistency model that corresponds to any implementation on a multiprocessor that uses write-buffers, even though we suspect that the sparc version 9 specification of relaxed memory order was intended to capture a general write-buffer architecture. The same technique is used to show that Coherence does not correspond to a write-buffer architecture. A corollary, which follows from the relationship between Coherence and Alpha, is that any implementation of Alpha consistency using write-buffers cannot produce all possible Alpha computations. That is, there are some computations that satisfy the Alpha specification but cannot occur in the given write-buffer implementation.

Self-Stabilizing Minimum Spanning Tree Construction on Message-Passing Networks

Self-stabilizing algorithms for constructing a spanning tree of an arbitrary network have been studied for many models of distributed networks including those that communicate via registers (either composite or read/write atomic) and those that employ message-passing. In contrast, much less has been done for the corresponding minimum spanning tree problem. The one published self-stabilizing distributed algorithm for the minimum spanning problem that we are aware of [3] assumes a composite atomicity model. This paper presents two minimum spanning tree algorithms designed directly for deterministic, message-passing networks. The first converts an arbitrary spanning tree to a minimum one; the second is a fully self-stabilizing construction. The algorithms assume distinct identifiers and reliable fifo message passing, but do not rely on a root or synchrony. Also, processors have a safe time-out mechanism (the minimum assumption necessary for a solution to exist.) Both algorithms apply to networks that can change dynamically.

Meeting times of random walks on graphs

We prove an upper bound on the meeting time of an arbitrary number of random walks in any connected undirected graph in terms of the meeting times of fewer random walks on the same graph. We show that the bound is tight for rings, and that it is both stronger and more general than a bound suggested by Tetali and Winkler (1991).

Limitations and capabilities of weak memory consistency systems

This dissertation develops and exploits a formalism for specifying memory consistency models. This formalism lays down the foundations for describing memory consistency models at various levels, and develops techniques to prove the equivalence between models defined at different levels. Two levels, called non-operational and operational, are addressed in this dissertation. The non-operational level describes these models in terms of program instructions or procedures, while the operational level describes them in terms of implementation events. Formal techniques are developed to prove the equivalence of rigorous specifications at both levels. This formalism is then exploited to define the memory consistency models of two state-of-the-art multiprocess systems: the SPARC version 8 architecture and the Java Virtual Machine. These models are defined at both operational and non-operational levels. These operational and non-operational descriptions are proved equivalent. The SPARC models provide “reasonably” weak memory consistency models that are capable of avoiding the use of explicit synchronization primitives for certain problems. However, Java provides a consistency model that is completely dependent on synchronization primitives, without which no form of coordination between different threads is possible. Fundamental process coordination problems have been extensively studied for traditional systems with strong memory consistency. This dissertation revisits the critical section and the producer/consumer problems in the context of weak memory consistency models. It establishes that the majority of known weak memory consistency models are incapable of supporting a solution to the critical section problem without the use of explicit synchronization primitives. Surprisingly, most of these models are capable of supporting solutions to versions of the producer/consumer problem without the use of these primitives.

Long-Lived, Fast, Waitfree Renaming with Optimal Name Space and High Throughput

The (n, k, l)-renaming problem requires that names from the set {1,..., l} are assigned to processes from a set of size n, provided that no more than k ≤ l processes axe simultaneously either holding or trying to acquire a name. A solution to this problem supplies a renaming object supporting both acquire and release operations so that no two processes ever simultaneously hold the same name. The protocol is waitfree if each participant successfully completes either operation in a bounded number of its own steps regardless of the speed of other processes; it is long-lived if it there is no bound on the number of operations that can be applied to the object; it is fast if the number of steps taken by any process before it completes an operation is independent of n; and it is name-space-optimal if l = k.

A simple, efficient algorithm for maximum finding on rings

The maximum finding problem is: given a network of processors with distinct identifiers, find that processor with the maximum identifier. We present a simple deterministic algorithm for maximum finding on asynchronous unidirectional rings that achieves the lowest worst-case complexity known for this model.

Maintaining B-trees on an EREW PRAM

Abstract Efficient and practical algorithms for maintaining general B -trees on an EREW PRAM are presented. Given a B -tree of order b with m distinct records, the search (respectively, insert and delete) problem for n input keys is solved on an n -processor EREW PRAM in O (log n + b log b m ) (respectively, O ( b (log n + log b m )) and O ( b 2 (log b n + log b m ))) time.

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O\sqrt n

O\sqrt n