47,449 research outputs found

    On the Optimal Space Complexity of Consensus for Anonymous Processes

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    The optimal space complexity of consensus in shared memory is a decades-old open problem. For a system of nn processes, no algorithm is known that uses a sublinear number of registers. However, the best known lower bound due to Fich, Herlihy, and Shavit requires Ω(n)\Omega(\sqrt{n}) registers. The special symmetric case of the problem where processes are anonymous (run the same algorithm) has also attracted attention. Even in this case, the best lower and upper bounds are still Ω(n)\Omega(\sqrt{n}) and O(n)O(n). Moreover, Fich, Herlihy, and Shavit first proved their lower bound for anonymous processes, and then extended it to the general case. As such, resolving the anonymous case might be a significant step towards understanding and solving the general problem. In this work, we show that in a system of anonymous processes, any consensus algorithm satisfying nondeterministic solo termination has to use Ω(n)\Omega(n) read-write registers in some execution. This implies an Ω(n)\Omega(n) lower bound on the space complexity of deterministic obstruction-free and randomized wait-free consensus, matching the upper bound and closing the symmetric case of the open problem

    Anonymous Obstruction-free (n,k)(n,k)-Set Agreement with n−k+1n-k+1 Atomic Read/Write Registers

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    The kk-set agreement problem is a generalization of the consensus problem. Namely, assuming each process proposes a value, each non-faulty process has to decide a value such that each decided value was proposed, and no more than kk different values are decided. This is a hard problem in the sense that it cannot be solved in asynchronous systems as soon as kk or more processes may crash. One way to circumvent this impossibility consists in weakening its termination property, requiring that a process terminates (decides) only if it executes alone during a long enough period. This is the well-known obstruction-freedom progress condition. Considering a system of nn {\it anonymous asynchronous} processes, which communicate through atomic {\it read/write registers only}, and where {\it any number of processes may crash}, this paper addresses and solves the challenging open problem of designing an obstruction-free kk-set agreement algorithm with (n−k+1)(n-k+1) atomic registers only. From a shared memory cost point of view, this algorithm is the best algorithm known so far, thereby establishing a new upper bound on the number of registers needed to solve the problem (its gain is (n−k)(n-k) with respect to the previous upper bound). The algorithm is then extended to address the repeated version of (n,k)(n,k)-set agreement. As it is optimal in the number of atomic read/write registers, this algorithm closes the gap on previously established lower/upper bounds for both the anonymous and non-anonymous versions of the repeated (n,k)(n,k)-set agreement problem. Finally, for 1 \leq x\leq k \textless{} n, a generalization suited to xx-obstruction-freedom is also described, which requires (n−k+x)(n-k+x) atomic registers only

    A Complexity-Based Hierarchy for Multiprocessor Synchronization

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    For many years, Herlihy's elegant computability based Consensus Hierarchy has been our best explanation of the relative power of various types of multiprocessor synchronization objects when used in deterministic algorithms. However, key to this hierarchy is treating synchronization instructions as distinct objects, an approach that is far from the real-world, where multiprocessor programs apply synchronization instructions to collections of arbitrary memory locations. We were surprised to realize that, when considering instructions applied to memory locations, the computability based hierarchy collapses. This leaves open the question of how to better capture the power of various synchronization instructions. In this paper, we provide an approach to answering this question. We present a hierarchy of synchronization instructions, classified by their space complexity in solving obstruction-free consensus. Our hierarchy provides a classification of combinations of known instructions that seems to fit with our intuition of how useful some are in practice, while questioning the effectiveness of others. We prove an essentially tight characterization of the power of buffered read and write instructions.Interestingly, we show a similar result for multi-location atomic assignments

    Communication Efficiency in Self-stabilizing Silent Protocols

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    Self-stabilization is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is self-stabilizing if it is able to recover without external intervention from any catastrophic transient failure. In this paper, our focus is to lower the communication complexity of self-stabilizing protocols \emph{below} the need of checking every neighbor forever. In more details, the contribution of the paper is threefold: (i) We provide new complexity measures for communication efficiency of self-stabilizing protocols, especially in the stabilized phase or when there are no faults, (ii) On the negative side, we show that for non-trivial problems such as coloring, maximal matching, and maximal independent set, it is impossible to get (deterministic or probabilistic) self-stabilizing solutions where every participant communicates with less than every neighbor in the stabilized phase, and (iii) On the positive side, we present protocols for coloring, maximal matching, and maximal independent set such that a fraction of the participants communicates with exactly one neighbor in the stabilized phase

    On the Uncontended Complexity of Anonymous Consensus

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    Consensus is one of the central distributed abstractions. By enabling a collection of processes to agree on one of the values they propose, consensus can be used to implement any generic replicated service in a consistent and fault-tolerant way. In this paper, we study uncontended complexity of anonymous consensus algorithms, counting the number of memory locations used and the number of memory updates performed in operations that encounter no contention. We assume that contention-free operations on a consensus object perform "fast" reads and writes, and resort to more expensive synchronization primitives, such as CAS, only when contention is detected. We call such concurrent implementations interval-solo-fast and derive one of the first nontrivial tight bounds on space complexity of anonymous interval-solo-fast consensus

    Towards formal models and languages for verifiable Multi-Robot Systems

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    Incorrect operations of a Multi-Robot System (MRS) may not only lead to unsatisfactory results, but can also cause economic losses and threats to safety. These threats may not always be apparent, since they may arise as unforeseen consequences of the interactions between elements of the system. This call for tools and techniques that can help in providing guarantees about MRSs behaviour. We think that, whenever possible, these guarantees should be backed up by formal proofs to complement traditional approaches based on testing and simulation. We believe that tailored linguistic support to specify MRSs is a major step towards this goal. In particular, reducing the gap between typical features of an MRS and the level of abstraction of the linguistic primitives would simplify both the specification of these systems and the verification of their properties. In this work, we review different agent-oriented languages and their features; we then consider a selection of case studies of interest and implement them useing the surveyed languages. We also evaluate and compare effectiveness of the proposed solution, considering, in particular, easiness of expressing non-trivial behaviour.Comment: Changed formattin

    Mean-Field-Type Games in Engineering

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    A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
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