13,285 research outputs found
Silent MST approximation for tiny memory
In network distributed computing, minimum spanning tree (MST) is one of the
key problems, and silent self-stabilization one of the most demanding
fault-tolerance properties. For this problem and this model, a polynomial-time
algorithm with memory is known for the state model. This is
memory optimal for weights in the classic range (where
is the size of the network). In this paper, we go below this
memory, using approximation and parametrized complexity.
More specifically, our contributions are two-fold. We introduce a second
parameter~, which is the space needed to encode a weight, and we design a
silent polynomial-time self-stabilizing algorithm, with space . In turn, this allows us to get an approximation algorithm for the problem,
with a trade-off between the approximation ratio of the solution and the space
used. For polynomial weights, this trade-off goes smoothly from memory for an -approximation, to memory for exact solutions,
with for example memory for a 2-approximation
Lock-in Problem for Parallel Rotor-router Walks
The rotor-router model, also called the Propp machine, was introduced as a
deterministic alternative to the random walk. In this model, a group of
identical tokens are initially placed at nodes of the graph. Each node
maintains a cyclic ordering of the outgoing arcs, and during consecutive turns
the tokens are propagated along arcs chosen according to this ordering in
round-robin fashion. The behavior of the model is fully deterministic. Yanovski
et al.(2003) proved that a single rotor-router walk on any graph with m edges
and diameter stabilizes to a traversal of an Eulerian circuit on the set of
all 2m directed arcs on the edge set of the graph, and that such periodic
behaviour of the system is achieved after an initial transient phase of at most
2mD steps. The case of multiple parallel rotor-routers was studied
experimentally, leading Yanovski et al. to the conjecture that a system of k
\textgreater{} 1 parallel walks also stabilizes with a period of length at
most steps. In this work we disprove this conjecture, showing that the
period of parallel rotor-router walks can in fact, be superpolynomial in the
size of graph. On the positive side, we provide a characterization of the
periodic behavior of parallel router walks, in terms of a structural property
of stable states called a subcycle decomposition. This property provides us the
tools to efficiently detect whether a given system configuration corresponds to
the transient or to the limit behavior of the system. Moreover, we provide
polynomial upper bounds of and on the
number of steps it takes for the system to stabilize. Thus, we are able to
predict any future behavior of the system using an algorithm that takes
polynomial time and space. In addition, we show that there exists a separation
between the stabilization time of the single-walk and multiple-walk
rotor-router systems, and that for some graphs the latter can be asymptotically
larger even for the case of walks
Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree
We present algorithms for distributed verification and silent-stabilization
of a DFS(Depth First Search) spanning tree of a connected network. Computing
and maintaining such a DFS tree is an important task, e.g., for constructing
efficient routing schemes. Our algorithm improves upon previous work in various
ways. Comparable previous work has space and time complexities of bits per node and respectively, where is the highest
degree of a node, is the number of nodes and is the diameter of the
network. In contrast, our algorithm has a space complexity of bits
per node, which is optimal for silent-stabilizing spanning trees and runs in
time. In addition, our solution is modular since it utilizes the
distributed verification algorithm as an independent subtask of the overall
solution. It is possible to use the verification algorithm as a stand alone
task or as a subtask in another algorithm. To demonstrate the simplicity of
constructing efficient DFS algorithms using the modular approach, We also
present a (non-sielnt) self-stabilizing DFS token circulation algorithm for
general networks based on our silent-stabilizing DFS tree. The complexities of
this token circulation algorithm are comparable to the known ones
Self-stabilizing tree algorithms
Designers of distributed algorithms have to contend with the problem of making the algorithms tolerant to several forms of coordination loss, primarily faulty initialization. The processes in a distributed system do not share a global memory and can only get a partial view of the global state. Transient failures in one part of the system may go unnoticed in other parts and thus cause the system to go into an illegal state. If the system were self-stabilizing, however, it is guaranteed that it will return to a legal state after a finite number of state transitions. This thesis presents and proves self-stabilizing algorithms for calculating tree metrics and for achieving mutual exclusion on a tree structured distributed system
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