876 research outputs found
Preserving Stabilization while Practically Bounding State Space
Stabilization is a key dependability property for dealing with unanticipated
transient faults, as it guarantees that even in the presence of such faults,
the system will recover to states where it satisfies its specification. One of
the desirable attributes of stabilization is the use of bounded space for each
variable. In this paper, we present an algorithm that transforms a stabilizing
program that uses variables with unbounded domain into a stabilizing program
that uses bounded variables and (practically bounded) physical time. While
non-stabilizing programs (that do not handle transient faults) can deal with
unbounded variables by assigning large enough but bounded space, stabilizing
programs that need to deal with arbitrary transient faults cannot do the same
since a transient fault may corrupt the variable to its maximum value. We show
that our transformation algorithm is applicable to several problems including
logical clocks, vector clocks, mutual exclusion, leader election, diffusing
computations, Paxos based consensus, and so on. Moreover, our approach can also
be used to bound counters used in an earlier work by Katz and Perry for adding
stabilization to a non-stabilizing program. By combining our algorithm with
that earlier work by Katz and Perry, it would be possible to provide
stabilization for a rich class of problems, by assigning large enough but
bounded space for variables.Comment: Moved some content from the Appendix to the main paper, added some
details to the transformation algorithm and to its descriptio
Optimal self-stabilizing mobile byzantine-tolerant regular register with bounded timestamps
This paper proposes the first implementation of a self-stabilizing regular register emulated by n servers that is tolerant to both Mobile Byzantine Agents and transient failures in a round-free synchronous model. Differently from existing Mobile Byzantine Tolerant register implementations, this paper considers a weaker model where: (i) the computation of the servers is decoupled from the movements of the Byzantine agents, i.e., movements may happen before, concurrently, or after the generation or the delivery of a message, and (ii) servers are not aware of their failure state i.e., they do not know if and when they have been corrupted by a Mobile Byzantine agent. The proposed protocol tolerates (i) any finite number of transient failures, and (ii) up to f Mobile Byzantine agents. In addition, our implementation uses bounded timestamps from the Z13 domain and it is optimal with respect to the number of servers needed to tolerate f Mobile Byzantine agents in the given model (i.e., n>6f when Δ=2δ, and n>8f when Δ=δ, where Δ represents the period at which the Byzantine agents move and δ is the upper bound on the communication latency)
Self-stabilizing TDMA Algorithms for Wireless Ad-hoc Networks without External Reference
Time division multiple access (TDMA) is a method for sharing communication
media. In wireless communications, TDMA algorithms often divide the radio time
into timeslots of uniform size, , and then combine them into frames of
uniform size, . We consider TDMA algorithms that allocate at least one
timeslot in every frame to every node. Given a maximal node degree, ,
and no access to external references for collision detection, time or position,
we consider the problem of collision-free self-stabilizing TDMA algorithms that
use constant frame size.
We demonstrate that this problem has no solution when the frame size is , where is the chromatic number for
distance- vertex coloring. As a complement to this lower bound, we focus on
proving the existence of collision-free self-stabilizing TDMA algorithms that
use constant frame size of . We consider basic settings (no hardware
support for collision detection and no prior clock synchronization), and the
collision of concurrent transmissions from transmitters that are at most two
hops apart. In the context of self-stabilizing systems that have no external
reference, we are the first to study this problem (to the best of our
knowledge), and use simulations to show convergence even with computation time
uncertainties
Stabilizing Byzantine-Fault Tolerant Storage
Distributed storage service is one of the main abstractions provided to developers of distributed applications due to its ability to hide the complexity generated by the various messages exchanged between processes. Many protocols have been proposed to build Byzantine-fault-tolerant (BFT) storage services on top of a message-passing system but none of them considers the possibility that well-behaving processes (i.e. correct processes) may experience transient failures due to, say, isolated errors during computation or bit alteration during message transfer. This paper proposes a stabilizing Byzantine-tolerant algorithm for emulating a multi-writer multi-reader regular register abstraction on top of a message passing system with n > 5f servers, which we prove to be the minimal possible number of servers for stabilizing and tolerating f Byzantine servers. That is, each read operation returns the value written by the most recent write and write operations are totally ordered with respect to the happened before relation. Our algorithm is particularly appealing for cloud computing architectures where both processors and memory contents (including stale messages in transit) are prone to errors, faults and malicious behaviors. The proposed implementation extends previous BFT implementations in two ways. First, the algorithm works even when the local memory of processors and the content of the communication channels are initially corrupted in an arbitrary manner. Second, unlike previous solutions, our algorithm uses bounded logical timestamps, a feature difficult to achieve in the presence of transient errors
Locally Self-Adjusting Skip Graphs
We present a distributed self-adjusting algorithm for skip graphs that
minimizes the average routing costs between arbitrary communication pairs by
performing topological adaptation to the communication pattern. Our algorithm
is fully decentralized, conforms to the model (i.e. uses
bit messages), and requires bits of memory for each
node, where is the total number of nodes. Upon each communication request,
our algorithm first establishes communication by using the standard skip graph
routing, and then locally and partially reconstructs the skip graph topology to
perform topological adaptation. We propose a computational model for such
algorithms, as well as a yardstick (working set property) to evaluate them. Our
working set property can also be used to evaluate self-adjusting algorithms for
other graph classes where multiple tree-like subgraphs overlap (e.g. hypercube
networks). We derive a lower bound of the amortized routing cost for any
algorithm that follows our model and serves an unknown sequence of
communication requests. We show that the routing cost of our algorithm is at
most a constant factor more than the amortized routing cost of any algorithm
conforming to our computational model. We also show that the expected
transformation cost for our algorithm is at most a logarithmic factor more than
the amortized routing cost of any algorithm conforming to our computational
model
A leader election algorithm for dynamic networks with causal clocks
An algorithm for electing a leader in an asynchronous network with dynamically changing communication topology is presented. The algorithm ensures that, no matter what pattern of topology changes occurs, if topology changes cease, then eventually every connected component contains a unique leader. The algorithm combines ideas from the Temporally Ordered Routing Algorithm for mobile ad hoc networks (Park and Corson in Proceedings of the 16th IEEE Conference on Computer Communications (INFOCOM), pp. 1405–1413 (1997) with a wave algorithm (Tel in Introduction to distributed algorithms, 2nd edn. Cambridge University Press, Cambridge, MA, 2000), all within the framework of a height-based mechanism for reversing the logical direction of communication topology links (Gafni and Bertsekas in IEEE Trans Commun C–29(1), 11–18 1981). Moreover, a generic representation of time is used, which can be implemented using totally-ordered values that preserve the causality of events, such as logical clocks and perfect clocks. A correctness proof for the algorithm is provided, and it is ensured that in certain well-behaved situations, a new leader is not elected unnecessarily, that is, the algorithm satisfies a stability condition.National Science Foundation (U.S.) (0500265)Texas Higher Education Coordinating Board (ARP-00512-0007-2006)Texas Higher Education Coordinating Board (ARP 000512-0130-2007)National Science Foundation (U.S.) (IIS-0712911)National Science Foundation (U.S.) (CNS-0540631)National Science Foundation (U.S.) (Research Experience for Undergraduates (Program) (0649233)
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