The distributed setting of this paper is an asynchronous system consisting of n processes prone to crashes and a number of shared read-write registers. We consider problems regarding assigning integer values to processes in an exclusive way, in the sense that no integer is assigned to two distinct processes. In the problem of renaming, any k ≤ n processes, that hold original names from a range [N] = {1,..., N}, contend to acquire unique integers as new names in a smaller range [M] using some r shared registers. When k and N are known, our wait-free solution operates in O(log k(log N + log k log log N)) local steps, for M = O(k), and with r = O(k log N) auxiliary shared registers. Processes obtain new k names by exploring their neighbors in bipartite graphs of suitable expansion properties, with nodes representing names and processes competing for the name of each visited node.} local steps are required in the worst case to wait-free solve renaming, when k and N are known and r and M are given constraints. We give a fully adaptive solution, with neither k nor N known, having M = 8k − lg k − 1 as a bound on the range of new names, operating in O(k) steps and using O(n 2) registers. We apply renaming algorithms to obtain solutions to the Store&Collect problem. When both k and N are known, then storing can be performed in O(log k(log N + log k log log N)) steps and collecting in O(k) steps, for r = O(k log(N/k)) registers. We consider the problem Unbounded-Naming in which processes repeatedly require new names, while no name can be reused once assigned, so that infinitely many integers need to be exclusively assigned as names. For no fixed integer i can one guarantee in a wait-free manner that i is eventually assigned to be a name, so some integers may never be used; the upper bound on the number of such unused integers is used as a measure of quality of a solution. We show that Unbounded-Naming is solvable in a non-blocking way with at most n −1 integers never assigned as names, which is best possible, and in a wait-free manner with at most n(n − 1) values never assigned as names.

In this paper we examine the general multi-word lock problem, where processes are allowed to multilock arbitrary registers. Aiming for a highly efficient solution we propose a randomized algorithm which successfully breaks long dependency chains, the crucial factor for slowing down an execution. In the analysis we focus on the 2-word lock problem and show that in this special case an execution of our algorithm takes with high probability at most time O( ∆ 3 log n / log log n), where n is the number of registers and ∆ the maximal number of processes interested in the same register (the contention). Furthermore, we implemented our algorithm for the general multi-word lock problem on an SGI Origin2000 machine, demonstrating that our algorithm is not only of theoretical interest.

Abstract. We introduce a novel term, memory-adaptive, that intuitively captures what it means for a distributed protocol to most efficiently make use of its shared memory. We also prove three results that relate to our memory-adaptive model. In our store/release protocols processors are required to store a value in shared MWMR memory so that it cannot be overwritten until it has been released by the processor. We show that there do not exist uniformly wait-free store/release protocols using only the basic operations read and write that are memory-adaptive to point contention. We further show that there exists a uniformly waitfree store/release protocol using only the basic operations read and write that is memory-adaptive to total contention. We finally show that there exists a uniformly wait-free store/release protocol using only the basic operations read, write, and write-plus that is memory-adaptive to interval contention and time-adaptive to total contention. 1

Abstract. Most people believe that renaming is easy: simply choose a name at random; if more than one process selects the same name, then try again. We highlight the issues that occur when trying to implement such a scheme and shed new light on the read-write complexity of randomized renaming in an asynchronous environment. At the heart of our new perspective stands an adaptive implementation of a randomized test-and-set object, that has poly-logarithmic step complexity per operation, with high probability. Interestingly, our implementation is anonymous, as it does not require process identifiers. Based on this implementation, we present two new randomized renaming algorithms. The first ensures a tight namespace of n names using O(n log 4 n) total steps, with high probability. This significantly improves on the complexity of the best previously known namespace-optimal algorithms. The second algorithm achieves a namespace of size k(1 + ɛ) using O(k log 4 k / log 2 (1 + ɛ)) total steps, both with high probability, where k is the total contention in the execution. It is the first adaptive randomized renaming algorithm, and it improves on existing deterministic solutions by providing a smaller namespace, and by lowering step complexity. 1

The classic renaming protocol of Moir and Anderson [4] uses a network of Θ(n 2) splitters to assign unique names to n processes with unbounded initial names. We show how to reduce this bound to Θ(n 3/2) splitters. 1

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In distributed computing, various different models exist. So far, the focus of the course was on loosely-coupled distributed systems such as the Internet, where nodes asynchronously communicate by exchanging messages. The “opposite” model is a tightly-coupled parallel computer where nodes access a common

(and return false), even if the value read by the load-link has since been restored. • The power of RMW operations can be measured with the so-called consensusnumber: The consensus-number k of a RMW operation defines whether one can solve consensus for k processes. Test-and-set for instance has consensus-number 2 (one can solve consensus with 2 processes, but not 3), whereas the consensus-number of compare-and-swap is infinite. It can be shown that the power of a shared memory system is determined by the consensus-number (“universality of consensus”.) This insight has a remarkable theoretical and practical impact. In practice for instance, after this was known, hardware designers stopped developing shared memory systems supporting weak RMW operations. • Many of the results derived in the message passing model have an equivalent in the shared memory model. Consensus for instance is traditionally studied in the shared memory model.