4,570 research outputs found
Distributed Computing with Adaptive Heuristics
We use ideas from distributed computing to study dynamic environments in
which computational nodes, or decision makers, follow adaptive heuristics (Hart
2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly
"best replying" to others' actions, and minimizing "regret", that have been
extensively studied in game theory and economics. We explore when convergence
of such simple dynamics to an equilibrium is guaranteed in asynchronous
computational environments, where nodes can act at any time. Our research
agenda, distributed computing with adaptive heuristics, lies on the borderline
of computer science (including distributed computing and learning) and game
theory (including game dynamics and adaptive heuristics). We exhibit a general
non-termination result for a broad class of heuristics with bounded
recall---that is, simple rules of behavior that depend only on recent history
of interaction between nodes. We consider implications of our result across a
wide variety of interesting and timely applications: game theory, circuit
design, social networks, routing and congestion control. We also study the
computational and communication complexity of asynchronous dynamics and present
some basic observations regarding the effects of asynchrony on no-regret
dynamics. We believe that our work opens a new avenue for research in both
distributed computing and game theory.Comment: 36 pages, four figures. Expands both technical results and discussion
of v1. Revised version will appear in the proceedings of Innovations in
Computer Science 201
A group membership algorithm with a practical specification
Presents a solvable specification and gives an algorithm for the group membership problem in asynchronous systems with crash failures. Our specification requires processes to maintain a consistent history in their sequences of views. This allows processes to order failures and recoveries in time and simplifies the programming of high level applications. Previous work has proven that the group membership problem cannot be solved in asynchronous systems with crash failures. We circumvent this impossibility result building a weaker, yet nontrivial specification. We show that our solution is an improvement upon previous attempts to solve this problem using a weaker specification. We also relate our solution to other methods and give a classification of progress properties that can be achieved under different models
Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms
In this paper, we investigate the approximate consensus problem in highly
dynamic networks in which topology may change continually and unpredictably. We
prove that in both synchronous and partially synchronous systems, approximate
consensus is solvable if and only if the communication graph in each round has
a rooted spanning tree, i.e., there is a coordinator at each time. The striking
point in this result is that the coordinator is not required to be unique and
can change arbitrarily from round to round. Interestingly, the class of
averaging algorithms, which are memoryless and require no process identifiers,
entirely captures the solvability issue of approximate consensus in that the
problem is solvable if and only if it can be solved using any averaging
algorithm. Concerning the time complexity of averaging algorithms, we show that
approximate consensus can be achieved with precision of in a
coordinated network model in synchronous
rounds, and in rounds when
the maximum round delay for a message to be delivered is . While in
general, an upper bound on the time complexity of averaging algorithms has to
be exponential, we investigate various network models in which this exponential
bound in the number of nodes reduces to a polynomial bound. We apply our
results to networked systems with a fixed topology and classical benign fault
models, and deduce both known and new results for approximate consensus in
these systems. In particular, we show that for solving approximate consensus, a
complete network can tolerate up to 2n-3 arbitrarily located link faults at
every round, in contrast with the impossibility result established by Santoro
and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1
link faults per round originating from the same node
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
Termination Detection of Local Computations
Contrary to the sequential world, the processes involved in a distributed
system do not necessarily know when a computation is globally finished. This
paper investigates the problem of the detection of the termination of local
computations. We define four types of termination detection: no detection,
detection of the local termination, detection by a distributed observer,
detection of the global termination. We give a complete characterisation
(except in the local termination detection case where a partial one is given)
for each of this termination detection and show that they define a strict
hierarchy. These results emphasise the difference between computability of a
distributed task and termination detection. Furthermore, these
characterisations encompass all standard criteria that are usually formulated :
topological restriction (tree, rings, or triangu- lated networks ...),
topological knowledge (size, diameter ...), and local knowledge to distinguish
nodes (identities, sense of direction). These results are now presented as
corollaries of generalising theorems. As a very special and important case, the
techniques are also applied to the election problem. Though given in the model
of local computations, these results can give qualitative insight for similar
results in other standard models. The necessary conditions involve graphs
covering and quasi-covering; the sufficient conditions (constructive local
computations) are based upon an enumeration algorithm of Mazurkiewicz and a
stable properties detection algorithm of Szymanski, Shi and Prywes
Dynamic FTSS in Asynchronous Systems: the Case of Unison
Distributed fault-tolerance can mask the effect of a limited number of
permanent faults, while self-stabilization provides forward recovery after an
arbitrary number of transient fault hit the system. FTSS protocols combine the
best of both worlds since they are simultaneously fault-tolerant and
self-stabilizing. To date, FTSS solutions either consider static (i.e. fixed
point) tasks, or assume synchronous scheduling of the system components. In
this paper, we present the first study of dynamic tasks in asynchronous
systems, considering the unison problem as a benchmark. Unison can be seen as a
local clock synchronization problem as neighbors must maintain digital clocks
at most one time unit away from each other, and increment their own clock value
infinitely often. We present many impossibility results for this difficult
problem and propose a FTSS solution when the problem is solvable that exhibits
optimal fault containment
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