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## Section: New Results

### Distributed Algorithms

#### One for All and All for One:Scalable Consensus in a Hybrid Communication Model

Participant : Michel Raynal.

This work [34] addresses consensus in an asynchronous model where the processes are partitioned into clusters. Inside each cluster, processes can communicate through a shared memory, which favors efficiency. Moreover, any pair of processes can also communicate through a message-passing communication system, which favors scalability. In such a “hybrid communication” context, the work presents two simple binary consensus algorithms (one based on local coins,the other one based on a common coin). These algorithms are straightforward extensions of existing message-passing randomized round-based consensus algorithms. At each round, the processes of each cluster first agree on the same value (using an underlying shared memory consensus algorithm), and then use a message-passing algorithm to converge on the same decided value. The algorithms are such that, if all except one processes of a cluster crash, the surviving process acts as if all the processes of its cluster were alive (hence the motto “one for all and all for one”). As a consequence, the hybrid communication model allows us to obtain simple, efficient, and scalable fault-tolerant consensus algorithms. As an important side effect, according to the size of each cluster, consensus can be obtained even if a majority of processes crash.

This work was done in collaboration with Jiannong Cao (Polytechnic University, Hong Kong).

#### Optimal Memory-Anonymous Symmetric Deadlock-Free Mutual Exclusion

Participant : Michel Raynal.

The notion of an anonymous shared memory (recently introduced in PODC 2017) considers that processes use different names for the same memory location. Hence, there is permanent disagreement on the location names among processes. In this context, the PODC paper presented -among other results- a symmetric deadlock-free mutual exclusion (mutex) algorithm for two processes and a necessary condition on the size m of the anonymous memory for the existence of a symmetric deadlock-free mutex algorithm in an n-process system. This work [22] answers several open problems related to symmetric deadlock-free mutual exclusion in an n-process system where the processes communicate through m registers. It first presents two algorithms. The first considers that the registers are anonymous read/write atomic registers and works for any m greater than 1 and belonging to the set M(n). It thus shows that this condition on m is both necessary and sufficient. The second algorithm considers anonymous read/modify/write atomic registers. It assumes that $m\in M\left(n\right)$. These algorithms differ in their design principles and their costs (measured as the number of registers which must contain the identity of a process to allow it to enter the critical section). The work also shows that the condition $m\in M\left(n\right)$ is necessary for deadlock-free mutex on top of anonymous read/modify/write atomic registers. It follows that, when m > 1, $m\in M\left(n\right)$ is a tight characterization of the size of the anonymous shared memory needed to solve deadlock-free mutex, be the anonymous registers read/write or read/modify/write.

This work was done in collaboration with Zahra Aghazadeh (University of Calgary), Damien Imbs (LIS, Université d’Aix-Marseille,CNRS, Université de Toulon), Gadi Taubenfeld (The Interdisciplinary Center of Herzliya) and Philipp Woelfel (University of Calgary).

#### Merkle Search Trees

Participants : Alex Auvolat, François Taïani.

Most recent CRDT (Conflict-free Replicated Data Type) techniques rely on a causal broadcast primitive to provide guarantees on the delivery of operation deltas. Such a primitive is unfortunately hard to implement efficiently in large open networks, whose membership is often difficult to track. As an alternative, we argue that pure state-based CRDTs can be efficiently implemented by encoding states as specialized Merkle trees, and that this approach is well suited to open networks where many nodes may join and leave. Indeed, Merkle trees enable efficient remote comparison and reconciliation of data sets, which can be used to implement the CRDT merge operator between two nodes without any prior information. This approach also does not require vector clock information, which would grow linearly with the number of participants.

At the core of our contribution [24] lies a new kind of Merkle tree, called Merkle Search Tree (MST), that implements a balanced search tree while maintaining key ordering. This latter property makes it particularly efficient in the case of updates on sets of sequential keys, a common occurrence in many applications. We use this new data structure to implement a distributed event store, and show its efficiency in very large systems with low rates of updates. In particular, we show that in some scenarios our approach is able to achieve both a 66% reduction of bandwidth cost over a vector-clock approach, as well as a 34% improvement in consistency level. We finally suggest other uses of our construction for distributed databases in open networks.

#### Dietcoin: Hardening Bitcoin Transaction Verification Process For Mobile Devices

Participants : Davide Frey, François Taïani.

Distributed ledgers are among the most replicated data repositories in the world. They offer data consistency, immutability, and auditability, based on the assumption that each participating node locally verifies their entire content. Although their content, currently extending up to a few hundred gigabytes, can be accommodated by dedicated commodity hard disks, downloading it, processing it, and storing it in general-purpose desktop and laptop computers can prove largely impractical. Even worse, this becomes a prohibitive restriction for smartphones, mobile devices, and resource-constrained IoT devices.

We carried out this work in collaboration with Pierre-Louis Roman, now at University of Lugano (Switzerland), as well as with Mark Makke from Vrije Universiteit, Amsterdam (the Netherlands), and Spyros Voulgaris from Athens University of Economics and Business (Greece).

Participants : Alex Auvolat, François Taïani, Michel Raynal.

Set-Constrained Delivery Broadcast (SCD-broadcast), recently introduced at ICDCN 2018, is a high-level communication abstraction that captures ordering properties not between individual messages but between sets of messages. More precisely, it allows processes to broadcast messages and deliver sets of messages, under the constraint that if a process delivers a set containing a message $m$ before a set containing a message ${m}^{\text{'}}$, then no other process delivers first a set containing ${m}^{\text{'}}$ and later a set containing $m$. It has been shown that SCD-broadcast and read/write registers are computationally equivalent, and an algorithm implementing SCD-broadcast is known in the context of asynchronous message passing systems prone to crash failures.

We introduce a Byzantine-tolerant SCD-broadcast algorithm in [23], which we call BSCD-broadcast. Our proposed algorithm assumes an underlying basic Byzantine-tolerant reliable broadcast abstraction. We first introduce an intermediary communication primitive, Byzantine FIFO broadcast (BFIFO-broadcast), which we then use as a primitive in our final BSCD-broadcast algorithm. Unlike the original SCD-broadcast algorithm that is tolerant to up to $t crashing processes, and unlike the underlying Byzantine reliable broadcast primitive that is tolerant to up to $t Byzantine processes, our BSCD-broadcast algorithm is tolerant to up to $t Byzantine processes. As an illustration of the high abstraction power provided by the BSCD-broadcast primitive, we show that it can be used to implement a Byzantine-tolerant read/write snapshot object in an extremely simple way.

#### PnyxDB: a Lightweight Leaderless Democratic Byzantine Fault Tolerant Replicated Datastore

Participants : Loïck Bonniot, François Taïani.

Byzantine-Fault-Tolerant (BFT) systems are rapidly emerging as a viable technology for production-grade systems, notably in closed consortia deployments for financial and supply-chain applications. Unfortunately, most algorithms proposed so far to coordinate these systems suffer from substantial scalability issues, mainly due to the requirement of a single leader node. We observed that many application workloads offer little concurrency, and proposed PnyxDB, an eventually-consistent BFT replicated datastore that exhibits both high scalability and low latency. Our approach (proposed in [40]) is based on conditional endorsements, that allow nodes to specify the set of transactions that must not be committed for the endorsement to be valid.

Additionally, although most of prior art rely on internal voting or quorum mechanisms, these mechanisms are not exposed to applications as first-class primitives. As a result, individual nodes cannot implement application-defined policies without additional effort, costs, and complexity. This is problematic, as application-level voting capabilities are key to a number of emerging decentralized BFT applications involving independent participants who need to balance conflicting goals and shared interests. In addition to its high scalability, PnyxDB supports application-level voting by design. We provided a comparison against BFTSMaRt and Tendermint, two competitors with different design aims, and demonstrated that our implementation speeds up commit latencies by a factor of 11, remaining below 5 seconds in a worldwide geodistributed deployment of 180 nodes.

PnyxDB's source code is freely available (https://github.com/technicolor-research/pnyxdb). This work has also been done in collaboration with Christoph Neumann at InterDigital.

#### Vertex Coloring with Communication Constraints in Synchronous Broadcast Networks

Participants : Hicham Lakhlef, Michel Raynal, François Taïani.

In this work [17], we consider distributed vertex-coloring in broadcast/receive networks suffering from conflicts and collisions. (A collision occurs when, during the same round, messages are sent to the same process by too many neighbors; a conflict occurs when a process and one of its neighbors broadcast during the same round.) More specifically, our work focuses on multi-channel networks, in which a process may either broadcast a message to its neighbors or receive a message from at most $\gamma$ of them. The work first provides a new upper bound on the corresponding graph coloring problem (known as frugal coloring) in general graphs, proposes an exact bound for the problem in trees, and presents a deterministic, parallel, color-optimal, collision- and conflict-free distributed coloring algorithm for trees, and proves its correctness.

#### Efficient Randomized Test-and-Set Implementations

Participant : George Giakkoupis.

In [16], we study randomized test-and-set (TAS) implementations from registers in the asynchronous shared memory model with $n$ processes. We introduce the problem of group election, a natural variant of leader election, and propose a framework for the implementation of TAS objects from group election objects. We then present two group election algorithms, each yielding an efficient TAS implementation. The first implementation has expected maxstep complexity $O\left({log}^{*}k\right)$ in the location-oblivious adversary model, and the second has expected maxstep complexity $O\left(loglogk\right)$ against any read/write-oblivious adversary, where $k\le n$ is the contention. These algorithms improve the previous upper bound by Alistarh and Aspnes (2011) of $O\left(loglogn\right)$ expected maxstep complexity in the oblivious adversary model.

We also propose a modification to a TAS algorithm by Alistarh, Attiya, Gilbert, Giurgiu, and Guerraoui (2010) for the strong adaptive adversary, which improves its space complexity from super-linear to linear, while maintaining its $O\left(logn\right)$ expected maxstep complexity. We then describe how this algorithm can be combined with any randomized TAS algorithm that has expected maxstep complexity $T\left(n\right)$ in a weaker adversary model, so that the resulting algorithm has $O\left(logn\right)$ expected maxstep complexity against any strong adaptive adversary and $O\left(T\left(n\right)\right)$ in the weaker adversary model.

Finally, we prove that for any randomized 2-process TAS algorithm, there exists a schedule determined by an oblivious adversary such that with probability at least $1/{4}^{t}$ one of the processes needs at least $t$ steps to finish its TAS operation. This complements a lower bound by Attiya and Censor-Hillel (2010) on a similar problem for $n\ge 3$ processes.

This work was done in collaboration with Philipp Woelfel (University of Calgary).