RoBuSt: A Crash-Failure-Resistant Distributed Storage System

In this work we present the first distributed storage system that is provably robust against crash failures issued by an adaptive adversary, i.e., for each batch of requests the adversary can decide based on the entire system state which servers will be unavailable for that batch of requests. Despite up to $\gamma n^{1/\log\log n}$ crashed servers, with $\gamma>0$ constant and $n$ denoting the number of servers, our system can correctly process any batch of lookup and write requests (with at most a polylogarithmic number of requests issued at each non-crashed server) in at most a polylogarithmic number of communication rounds, with at most polylogarithmic time and work at each server and only a logarithmic storage overhead. Our system is based on previous work by Eikel and Scheideler (SPAA 2013), who presented IRIS, a distributed information system that is provably robust against the same kind of crash failures. However, IRIS is only able to serve lookup requests. Handling both lookup and write requests has turned out to require major changes in the design of IRIS.Comment: Revised full versio

Parallel Batch-Dynamic Graph Connectivity

In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic connectivity is the elegant level-set algorithm of Holm, de Lichtenberg and Thorup (HDT), which achieves $O(\log^2 n)$ amortized time per edge insertion or deletion, and $O(\log n / \log\log n)$ time per query. We design a parallel batch-dynamic connectivity algorithm that is work-efficient with respect to the HDT algorithm for small batch sizes, and is asymptotically faster when the average batch size is sufficiently large. Given a sequence of batched updates, where $\Delta$ is the average batch size of all deletions, our algorithm achieves $O(\log n \log(1 + n / \Delta))$ expected amortized work per edge insertion and deletion and $O(\log^3 n)$ depth w.h.p. Our algorithm answers a batch of $k$ connectivity queries in $O(k \log(1 + n/k))$ expected work and $O(\log n)$ depth w.h.p. To the best of our knowledge, our algorithm is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Adaptive Regret Minimization in Bounded-Memory Games

Online learning algorithms that minimize regret provide strong guarantees in situations that involve repeatedly making decisions in an uncertain environment, e.g. a driver deciding what route to drive to work every day. While regret minimization has been extensively studied in repeated games, we study regret minimization for a richer class of games called bounded memory games. In each round of a two-player bounded memory-m game, both players simultaneously play an action, observe an outcome and receive a reward. The reward may depend on the last m outcomes as well as the actions of the players in the current round. The standard notion of regret for repeated games is no longer suitable because actions and rewards can depend on the history of play. To account for this generality, we introduce the notion of k-adaptive regret, which compares the reward obtained by playing actions prescribed by the algorithm against a hypothetical k-adaptive adversary with the reward obtained by the best expert in hindsight against the same adversary. Roughly, a hypothetical k-adaptive adversary adapts her strategy to the defender's actions exactly as the real adversary would within each window of k rounds. Our definition is parametrized by a set of experts, which can include both fixed and adaptive defender strategies. We investigate the inherent complexity of and design algorithms for adaptive regret minimization in bounded memory games of perfect and imperfect information. We prove a hardness result showing that, with imperfect information, any k-adaptive regret minimizing algorithm (with fixed strategies as experts) must be inefficient unless NP=RP even when playing against an oblivious adversary. In contrast, for bounded memory games of perfect and imperfect information we present approximate 0-adaptive regret minimization algorithms against an oblivious adversary running in time n^{O(1)}.Comment: Full Version. GameSec 2013 (Invited Paper

Distributed Computing in the Asynchronous LOCAL model

The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in lock steps, and are failure-free. We show that relaxing these hypotheses to some extent does not hurt local computing. In particular, we show that, for any construction task $T$ associated to a locally checkable labeling (LCL), if $T$ is solvable in $t$ rounds in the LOCAL model, then $T$ remains solvable in $O(t)$ rounds in the asynchronous LOCAL model. This improves the result by Casta\~neda et al. [SSS 2016], which was restricted to 3-coloring the rings. More generally, the main contribution of this paper is to show that, perhaps surprisingly, asynchrony and failures in the computations do not restrict the power of the LOCAL model, as long as the communications remain synchronous and failure-free

Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log \Delta)$ bits per node and $O(nD)$ respectively, where $\Delta$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

Snap-Stabilization in Message-Passing Systems

In this paper, we tackle the open problem of snap-stabilization in message-passing systems. Snap-stabilization is a nice approach to design protocols that withstand transient faults. Compared to the well-known self-stabilizing approach, snap-stabilization guarantees that the effect of faults is contained immediately after faults cease to occur. Our contribution is twofold: we show that (1) snap-stabilization is impossible for a wide class of problems if we consider networks with finite yet unbounded channel capacity; (2) snap-stabilization becomes possible in the same setting if we assume bounded-capacity channels. We propose three snap-stabilizing protocols working in fully-connected networks. Our work opens exciting new research perspectives, as it enables the snap-stabilizing paradigm to be implemented in actual networks

Local algorithms : Self-stabilization on speed

Non peer reviewe

Self-Stabilizing Byzantine Asynchronous Unison

We explore asynchronous unison in the presence of systemic transient and permanent Byzantine faults in shared memory. We observe that the problem is not solvable under less than strongly fair scheduler or for system topologies with maximum node degree greater than two. We present a self-stabilizing Byzantine-tolerant solution to asynchronous unison for chain and ring topologies. Our algorithm has minimum possible containment radius and optimal stabilization time