We consider the problem of waking up n processors in a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to processors and with or without labeling of processors. The main question we answer is: how fast we can wake all the processors up with probability 1-e in each of these eight models. In [11] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n/logn). We also show logarithmic or polylogarithmic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.

This paper studies the differences between two levels of synchronization in a distributed broadcast system (or a multiple access channel). In the globally synchronous model, all processors have access to a global clock. In the locally synchronous model, processors have local clocks ticking at the same rate, but each clock starts individually, when the processor wakes up. We consider the fundamental problem of waking up all of n processors of a completely connected broadcast system. Some processors wake up spontaneously, while others have to be woken up. Only wake processors can...

We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.

We present an improved algorithm to wake up a multi-hop ad-hoc radio network. The goal is to have all the nodes activated, when some of them may wake up spontaneously at arbitrary times and the remaining nodes need to be awoken by the already active ones. The best previously known wake-up algorithm was given by Chrobak, G¸asieniec and Kowalski [11], and operated in time O(n 5/3 log n), where n is the number of nodes. We give an algorithm with the running time O(n 3/2 log n). This also yields better algorithms for other synchronization-type primitives, like leader election and local-clocks synchronization, each with a time performance that differs from that of wake-up by an extra factor of O(log n) only, and improves the best previously known method for the problem by a factor of n 1/6. A wakeup algorithm is a schedule of transmissions for each node. It can be represented as a collection of binary sequences. Useful properties of such collections have been abstracted to define a (radio) synchronizer. It has been known that good radio synchronizers exist and previous algorithms [17, 11] relied on this. We show how to construct such synchronizers in polynomial time, from suitable constructible expanders. As an application, we obtain a wake-up protocol for a multiple-access channel that activates the network in time O(k 2 polylog n), where k is the number of stations that wake up spontaneously, and which can be found in time polynomial in n. We extend the notion of synchronizers to universal synchronizers. We show that there exist universal synchronizers with parameters that guarantee time O(n 3/2 log n) of wake-up.

In the totally anonymous shared memory model of asynchronous distributed computing, processes have no id's and run identical programs. Moreover, processes have identical interface to the shared memory, and in particular, there are no single-writer registers. This paper assumes that processes do not fail, and the shared memory consists only of read/write registers, which are initialized to some default value. A complete characterization of the functions and relations that can be computed within this model is presented. The consensus problem is an important relation which can be computed. Unlike functions, which can be computed with two registers, the consensus protocol uses a linear number of shared registers and rounds. The paper proves logarithmic lower bounds on the number of registers and rounds needed for solving consensus in this model, indicating the d...

Many recent wait-free implementations are based on a sharedmemory that supports a pair of synchronization operations, known as LL and SC. In this paper, we establish an intrinsic performance limitation of these operations: even the simple wakeup problem [16], which requires some process to detect that all n processes are up, cannot be solved unless some process performs#for n) shared-memory operations. Using this basic result, we derive a#230 n) lower bound on the worst-case shared-access time complexity of n-process implementations of several types of objects, including fetch&increment, fetch&multiply, fetch&and, queue, and stack. (The worst-case shared-access time complexity of an implementation is the number of shared-memory operations that a process performs, in the worst-case, in order to complete a single operation on the implementation.) Our lower bound is strong in several ways: it holds even if (1) shared-memory has an infinite number of words, each of unbounded size, (2) sh...

This paper investigates the effects of the failure of shared objects on distributed systems. First the notion of a faulty shared object is introduced. Then upper and lower bounds on the space complexity of implementing reliable shared objects are provided.

Abstract. This paper presents lower bounds on the time- and spacecomplexity of implementations that use the k compare-and-swap (k-CAS) synchronization primitives. We prove that the use of k-CAS primitives cannot improve neither the time- nor the space-complexity of implementations of widely-used concurrent objects, such as counter, stack, queue, and collect. Surprisingly, the use of k-CAS may even increase the space complexity required by such implementations. We prove that the worst-case average number of steps performed by processes for any n-process implementation of a counter, stack or queue object is Ω(log k+1 n), even if the implementation can use j-CAS for j ≤ k. This bound holds even if a k-CAS operation is allowed to read the k values of the objects it accesses and return these values to the calling process. This bound is tight. We also consider more realistic non-reading k-CAS primitives. An operation of a non-reading k-CAS primitive is only allowed to return a success/failure indication. For implementations of the collect object that use such primitives, we prove that the worst-case average number of steps performed by processes is Ω(log 2 n), regardless of the value of k. This implies a round complexity lower bound of Ω(log 2 n) for such implementations. As there is an O(log 2 n) round complexity implementation of collect that uses only reads and writes, these results establish that non-reading k-CAS is no stronger than read and write for collect implementation round complexity. We also prove that k-CAS does not improve the space complexity of implementing many objects (including counter, stack, queue, and singlewriter snapshot). An implementation has to use at least n base objects even if k-CAS is allowed, and if all operations (other than read) swap exactly k base objects, then the space complexity must be at least k · n. 1

We consider a distributed environment consisting of n processors that need to perform t tasks. We assume that communication is initially unavailable and that processors begin work in isolation. At some unknown point of time an unknown collection of processors may establish communication. Before processors begin communication they execute tasks in the order given by their schedules. Our goal is to schedule work of isolated processors so that when communication is established for the rst time, the number of redundantly executed tasks is controlled. We quantify worst case redundancy as a function of processor advancements through their schedules. In this work we rene and simplify an extant deterministic construction for schedules with n t, and we develop a new analysis of its waste. The new analysis shows that for any pair of schedules, the number of redundant tasks can be controlled for the entire range of t tasks. Our new result is asymptotically optimal: the tails of these schedules are within a 1 +O(n 1 4 ) factor of the lower bound. We also present two new deterministic constructions one for t n, and the other for t n 3=2 , which substantially improve pairwise waste for all prexes of length t= p n, and oer near optimal waste for the tails of the schedules. Finally, we present bounds for waste of any collection of k 2 processors for both deterministic and randomized constructions. 1

Worst-case time complexity is a measure of the maximumtime needed to solve a problem over all runs. Contention-free time complexity indicates the maximum time needed when a process executes by itself, without competition from other processes. Since contention is rare in well-designed systems, it is important to design algorithms which perform well in the absence of contention. We study the contention-free time complexity of shared memory algorithms using two measures: step complexity, which counts the number of accesses to shared registers; and register complexity, which measures the number of different registers accessed. Depending on the system architecture, one of the two measures more accurately reflects the elapsed time. We provide lower and upper bounds for the contention-free step and register complexity of solving the mutual exclusion problem as a function of the number of processes and the size of the largest register that can be accessed in one atomic step. We also present bo...