105 research outputs found
Self-Stabilizing Token Distribution with Constant-Space for Trees
Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most l tokens. Our goal is to distribute the tokens in the whole network so that every process holds exactly k tokens. In the initial configuration, the total number of tokens in the network may not be equal to nk where n is the number of processes in the network. The root process is given the ability to create a new token or remove a token from the network. We aim to minimize the convergence time, the number of token moves, and the space complexity. A self-stabilizing token distribution algorithm that converges within O(n l) asynchronous rounds and needs Theta(nh epsilon) redundant (or unnecessary) token moves is given, where epsilon = min(k,l-k) and h is the height of the tree network. Two novel ideas to reduce the number of redundant token moves are presented. One reduces the number of redundant token moves to O(nh) without any additional costs while the other reduces the number of redundant token moves to O(n), but increases the convergence time to O(nh l). All algorithms given have constant memory at each process and each link register
Loosely-Stabilizing Leader Election on Arbitrary Graphs in Population Protocols Without Identifiers nor Random Numbers
In the population protocol model Angluin et al. proposed in 2004, there exists no self-stabilizing leader election protocol for complete graphs, arbitrary graphs, trees, lines, degree-bounded graphs and so on unless the protocol knows the exact number of nodes. To circumvent the impossibility, we introduced the concept of loose-stabilization in 2009, which relaxes the closure requirement of self-stabilization. A loosely-stabilizing protocol guarantees that starting from any initial configuration a system reaches a safe configuration, and after that, the system keeps its specification (e.g. the unique leader) not forever, but for a sufficiently long time (e.g. exponentially large time with respect to the number of nodes). Our previous works presented two loosely-stabilizing leader election protocols for arbitrary graphs; One uses agent identifiers and the other uses random numbers to elect a unique leader. In this paper, we present a loosely-stabilizing protocol that solves leader election on arbitrary graphs without agent identifiers nor random numbers. By the combination of virus-propagation and token-circulation, the proposed protocol achieves polynomial convergence time and exponential holding time without such external entities. Specifically, given upper bounds N and Delta of the number of nodes n and the maximum degree of nodes delta respectively, it reaches a safe configuration within O(m*n^3*d + m*N*Delta^2*log(N)) expected steps, and keeps the unique leader for Omega(N*e^N) expected steps where m is the number of edges and d is the diameter of the graph. To measure the time complexity of the protocol, we assume the uniformly random scheduler which is widely used in the field of the population protocols
Brief Announcement: Loosely-stabilizing Leader Election with Polylogarithmic Convergence Time
We present a fast loosely-stabilizing leader election protocol in the population protocol model. It elects a unique leader in a poly-logarithmic time and holds the leader for a polynomial time with arbitrarily large degree in terms of parallel time, i.e, the number of steps per the population size
On Asynchrony, Memory, and Communication: Separations and Landscapes
Research on distributed computing by a team of identical mobile computational
entities, called robots, operating in a Euclidean space in
-- () cycles, has
recently focused on better understanding how the computational power of robots
depends on the interplay between their internal capabilities (i.e., persistent
memory, communication), captured by the four standard computational models
(OBLOT, LUMI, FSTA, and FCOM) and the conditions imposed by the external
environment, controlling the activation of the robots and their synchronization
of their activities, perceived and modeled as an adversarial scheduler.
We consider a set of adversarial asynchronous schedulers ranging from the
classical semi-synchronous (SSYNCH) and fully asynchronous (ASYNCH) settings,
including schedulers (emerging when studying the atomicity of the combination
of operations in the cycles) whose adversarial power is in
between those two. We ask the question: what is the computational relationship
between a model under adversarial scheduler () and a
model under scheduler ()? For example, are the robots in
more powerful (i.e., they can solve more problems) than those in
?
We answer all these questions by providing, through cross-model analysis, a
complete characterization of the computational relationship between the power
of the four models of robots under the considered asynchronous schedulers. In
this process, we also provide qualified answers to several open questions,
including the outstanding one on the proper dominance of SSYNCH over ASYNCH in
the case of unrestricted visibility
Self-Stabilizing Construction of a Minimal Weakly -Reachable Directed Acyclic Graph
We propose a self-stabilizing algorithm to construct a minimal weakly
-reachable directed acyclic graph (DAG), which is suited for
routing messages on wireless networks. Given an arbitrary, simple, connected,
and undirected graph and two sets of nodes, senders and targets , a directed subgraph
of is a weakly -reachable DAG on , if
is a DAG and every sender can reach at least one target, and every target is
reachable from at least one sender in . We say that a weakly
-reachable DAG on is minimal if any proper subgraph
of is no longer a weakly -reachable DAG. This DAG is a
relaxed version of the original (or strongly) -reachable DAG,
where every target is reachable from every sender. This is because a strongly
-reachable DAG does not always exist; some graph has no
strongly -reachable DAG even in the case
. On the other hand, the proposed algorithm
always constructs a weakly -reachable DAG for any
and . Furthermore, the proposed algorithm is self-stabilizing;
even if the constructed DAG deviates from the reachability requirement by a
breakdown or exhausting the battery of a node having an arc in the DAG, this
algorithm automatically reconstructs the DAG to satisfy the requirement again.
The convergence time of the algorithm is asynchronous rounds, where
is the diameter of a given graph. We conduct small simulations to evaluate the
performance of the proposed algorithm. The simulation result indicates that its
execution time decreases when the number of sender nodes or target nodes is
large
- …