1,106 research outputs found
Leader Election in Anonymous Rings: Franklin Goes Probabilistic
We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size
Memory lower bounds for deterministic self-stabilization
In the context of self-stabilization, a \emph{silent} algorithm guarantees
that the register of every node does not change once the algorithm has
stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that,
for finding the centers of a graph, for electing a leader, or for constructing
a spanning tree, every silent algorithm must use a memory of
bits per register in -node networks. Similarly, Korman et al. [Dist. Comp.
'07] proved, using the notion of proof-labeling-scheme, that, for constructing
a minimum-weight spanning trees (MST), every silent algorithm must use a memory
of bits per register. It follows that requiring the algorithm
to be silent has a cost in terms of memory space, while, in the context of
self-stabilization, where every node constantly checks the states of its
neighbors, the silence property can be of limited practical interest. In fact,
it is known that relaxing this requirement results in algorithms with smaller
space-complexity.
In this paper, we are aiming at measuring how much gain in terms of memory
can be expected by using arbitrary self-stabilizing algorithms, not necessarily
silent. To our knowledge, the only known lower bound on the memory requirement
for general algorithms, also established at the end of the 90's, is due to
Beauquier et al.~[PODC '99] who proved that registers of constant size are not
sufficient for leader election algorithms. We improve this result by
establishing a tight lower bound of bits per
register for self-stabilizing algorithms solving -coloring or
constructing a spanning tree in networks of maximum degree~. The lower
bound bits per register also holds for leader election
Communication cost of consensus for nodes with limited memory
Motivated by applications in blockchains and sensor networks, we consider a
model of nodes trying to reach consensus on their majority bit. Each node
is assigned a bit at time zero, and is a finite automaton with bits of
memory (i.e., states) and a Poisson clock. When the clock of rings,
can choose to communicate, and is then matched to a uniformly chosen node
. The nodes and may update their states based on the state of the
other node. Previous work has focused on minimizing the time to consensus and
the probability of error, while our goal is minimizing the number of
communications. We show that when , consensus can be
reached at linear communication cost, but this is impossible if
. We also study a synchronous variant of the model, where
our upper and lower bounds on for achieving linear communication cost are
and , respectively. A key step is to
distinguish when nodes can become aware of knowing the majority bit and stop
communicating. We show that this is impossible if their memory is too low.Comment: 62 pages, 5 figure
Leader election in synchronous networks
Worst, best and average number of messages and running time of leader election algorithms of different distributed systems are analyzed. Among others the known characterizations of the expected number of messages for LCR algorithm and of the worst number of messages of Hirschberg-Sinclair algorithm are improve
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