38 research outputs found
Anonymous Obstruction-free -Set Agreement with Atomic Read/Write Registers
The -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
different values are decided. This is a hard problem in the sense that it
cannot be solved in asynchronous systems as soon as 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 {\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 -set agreement algorithm with 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 with respect to the
previous upper bound). The algorithm is then extended to address the repeated
version of -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 -set agreement problem. Finally, for 1 \leq x\leq k
\textless{} n, a generalization suited to -obstruction-freedom is also
described, which requires atomic registers only
Optimal byzantine resilient convergence in oblivious robot networks
Given a set of robots with arbitrary initial location and no agreement on a
global coordinate system, convergence requires that all robots asymptotically
approach the exact same, but unknown beforehand, location. Robots are
oblivious-- they do not recall the past computations -- and are allowed to move
in a one-dimensional space. Additionally, robots cannot communicate directly,
instead they obtain system related information only via visual sensors. We draw
a connection between the convergence problem in robot networks, and the
distributed \emph{approximate agreement} problem (that requires correct
processes to decide, for some constant , values distance
apart and within the range of initial proposed values). Surprisingly, even
though specifications are similar, the convergence implementation in robot
networks requires specific assumptions about synchrony and Byzantine
resilience. In more details, we prove necessary and sufficient conditions for
the convergence of mobile robots despite a subset of them being Byzantine (i.e.
they can exhibit arbitrary behavior). Additionally, we propose a deterministic
convergence algorithm for robot networks and analyze its correctness and
complexity in various synchrony settings. The proposed algorithm tolerates f
Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks,
(3f+1)-sized in semi-synchronous networks. These bounds are optimal for the
class of cautious algorithms, which guarantee that correct robots always move
inside the range of positions of the correct robots
RoboCast: Asynchronous Communication in Robot Networks
This paper introduces the \emph{RoboCast} communication abstraction. The
RoboCast allows a swarm of non oblivious, anonymous robots that are only
endowed with visibility sensors and do not share a common coordinate system, to
asynchronously exchange information. We propose a generic framework that covers
a large class of asynchronous communication algorithms and show how our
framework can be used to implement fundamental building blocks in robot
networks such as gathering or stigmergy. In more details, we propose a RoboCast
algorithm that allows robots to broadcast their local coordinate systems to
each others. Our algorithm is further refined with a local collision avoidance
scheme. Then, using the RoboCast primitive, we propose algorithms for
deterministic asynchronous gathering and binary information exchange
Certified Impossibility Results for Byzantine-Tolerant Mobile Robots
We propose a framework to build formal developments for robot networks using
the COQ proof assistant, to state and to prove formally various properties. We
focus in this paper on impossibility proofs, as it is natural to take advantage
of the COQ higher order calculus to reason about algorithms as abstract
objects. We present in particular formal proofs of two impossibility results
forconvergence of oblivious mobile robots if respectively more than one half
and more than one third of the robots exhibit Byzantine failures, starting from
the original theorems by Bouzid et al.. Thanks to our formalization, the
corresponding COQ developments are quite compact. To our knowledge, these are
the first certified (in the sense of formally proved) impossibility results for
robot networks
Brief Announcement: Anonymous Obstruction-free (n, k)-Set Agreement with n−k+1 Atomic Read/Write Registers
International audienceThis paper presents an obstruction-free solution to the (n,k)-set agreement problem in an asynchronous anonymous read/write system using solely (n − k + 1) registers. We then extend this algorithm into (i) a space-optimal solution for the repeated version of (n, k)-set agreement, and (ii) an x-obstruction- free solution using (n − k + x) atomic registers (with 1 ≤ x ≤ k < n)
Certified Impossibility Results for Byzantine-Tolerant Mobile Robots
We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks
(anti−Ω x ×Σz)-based k-set Agreement Algorithms
This paper considers the k-set agreement problem in a crash-prone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti−Ω k and the weak-quorum class Σk. The paper investigates the families of failure detector (anti−Ω x)1≤x≤n and (Σz)1≤z≤n. It characterizesin an n processes system equipped with failure detectors anti−Ω x and Σz for which values of k,x and z k-set-agreement can be solved. While doing so, the paper (1) disproves previous conjunctures about the weakest failure detector to solve k-set-agreement in the asynchronous message passing model and, (2) introduces the first indulgent algorithm that tolerates a majority of processes failures. Keywords: Set-agreement, asynchrony, failure detectors, indulgent algorithms.
Parallel Consensus is Harder than Set Agreement in Message Passing
International audienceIn the traditional consensus task, processes are required to agree on a common value chosen among the initial values of the participating processes. It is well known that consensus cannot be solved in crash-prone, asynchronous distributed systems. Two generalizations of the consensus tasks have been introduced: k-set agreement and k-parallel consensus. The k-set agreement task has the same requirements as consensus except that processes are allowed to decide up to k distinct values. In the k-parallel consensus task, each process participates simultaneously in k instances of consensus and is required to decide in at least one of them; any two processes deciding in the same instance must decide the same value. It is known that both tasks are equivalent in the wait-free shared memory model. Perhaps surprisingly, this paper shows that this is no longer the case in the n-process asynchronous message passing model with at most t process crashes. Specifically, the paper establishes that for parameters t, n, k such that t > n+k−2 , k-parallel consensus is strictly harder than k-set 2 agreement. The proof compares the information on failures necessary to solve each task in the failure detector framework and relies on a result in topological combinatorics, namely, the chromatic number of Kneser graphs. The paper also introduces the new failure detector class V Σk , which is a generalization of the quorum failures detector class Σ suited to k-parallel consensus