Thibault Rieutord

Perfect Failure Detection with Very Few Bits

A failure detector is a distributed oracle that provides each process with a module that continuously outputs an estimate of which processes in the system have failed. The perfect failure detector provides accurate and eventually complete information about process failures. We show that, in asynchronous failure-prone message-passing systems, perfect failure detection can be achieved by an oracle that outputs at most \(\lceil \log \alpha (n)\rceil +1\) bits per process in n-process systems, where \(\alpha \) denotes the inverse-Ackermann function. This result is essentially optimal, as we also show that, in the same environment, no failure detector outputting a constant number of bits per process can achieve perfect failure detection.

A Failure Detector for k-Set Agreement in Dynamic Systems

The k-set agreement problem is a generalization of the consensus problem where processes can decide up to k different values. Very few papers have tackled this problem in dynamic networks, and to the best of our knowledge, every algorithm proposed so far for k-set agreement in dynamic networks assumed synchronous communications or made strong failure pattern assumptions. Exploiting the formalism of the Time-Varying Graph model, this paper proposes a new quorum-based failure detector for solving k-set agreement in dynamic networks with asynchronous communications. We present two algorithms that implement this new failure detector using graph connectivity and message pattern assumptions. We also provide an algorithm for solving k-set agreement using our new failure detector.

An Asynchronous Computability Theorem for Fair Adversaries

This paper proposes a simple topological characterization of a large class of fair adversarial models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a model in the class is precisely captured by iterations of the corresponding affine task. Fair adversaries include, but are not restricted to, the models of wait-freedom, t-resilience, and k-concurrency. Our results generalize and improve all previously derived topological characterizations of the ability of a model to solve distributed tasks.

Progress-Space Tradeoffs in Single-Writer Memory Implementations

Most algorithms designed for shared-memory distributed systems assume the single-writer multi-reader (SWMR) setting where each process is provided with a unique register readable by all. In a system where computation is performed by a bounded number n of processes coming from a very large (possibly unbounded) set of potential participants, the assumption of a SWMR memory is no longer reasonable. If only a bounded number of multi-writer multi-reader (MWMR) registers are provided, we cannot rely on an a priori assignment of processes to registers. In this setting, simulating SWMR memory, or equivalently, ensuring stable writing (i.e., every written value persists in the memory), is desirable. In this paper, we propose a SWMR simulation that adapts the number of MWMR registers used to the desired progress condition. For any given k from 1 to n, we present an algorithm that uses only n+k-1 registers to simulate a k-lock-free SWMR memory. We also give a matching lower bound of n+1 registers required for the case of 2-lock-freedom, which supports our conjectures that the algorithm is space-optimal. Our lower bound holds for the strictly weaker progress condition of 2-obstruction-freedom, which suggests that the space complexity for k-obstruction-free and k-lock-free SWMR simulations might coincide.

Brief Announcement: Compact Topology of Shared-Memory Adversaries

The paper proposes a simple topological characterization of a large class of adversarial distributed-computing models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a model in the class is precisely captured by iterations of the corresponding affine task. While an adversary is in general defined as a non-compact set of infinite runs, its affine task is just a finite subset of runs of the 2-round iterated immediate snapshot (IIS) model. Our results generalize and improve all previously derived topological characterizations of distributed-computing models.

Agreement Functions for Distributed Computing Models

The paper proposes a surprisingly simple characterization of a large class of models of distributed computing, via an agreement function: for each set of processes, the function determines the best level of set consensus these processes can reach. We show that the task computability of a large class of fair adversaries that includes, in particular superset-closed and symmetric one, is precisely captured by agreement functions.