The contribution of this paper is threefold. First, we present the paradigm of snap-stabilization. A snap-stabilizing protocol guarantees that, starting from an arbitrary system configuration, the protocol always beha...
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The contribution of this paper is threefold. First, we present the paradigm of snap-stabilization. A snap-stabilizing protocol guarantees that, starting from an arbitrary system configuration, the protocol always behaves according to its specification. So, a snap-stabilizing protocol is a time optimal self-stabilizing protocol (because it stabilizes in 0 rounds). Second, we propose a new Propagation of Information with Feedback (PIF) cycle, called Propagation of Information with Feedback and Cleaning (PFC). We show three different implementations of this new PIF. The first one is a basic PFC cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h(2)) rounds (where h is the height of the tree) due to some undesirable local states. The second algorithm improves the worst delay of the basic PFC algorithm from O(h(2)) to 1 round. The state requirement for the above two algorithms is 3 states per processor, except for the root and leaf processors that use only 2 states. Also, they work on oriented trees. We then propose a third snap-stabilizing PIF algorithm on un-oriented tree networks. The state requirement of the third algorithm depends on the degree of the processors, and the delay is at most h rounds. Next, we analyze the maximum waiting time before a PIF cycle can be initiated whether the PIF cycle is infinitely and sequentially repeated or launch as an isolated PIF cycle. The analysis is made for both oriented and un-oriented trees. We show or conjecture that the two best of the above algorithms produce optimal waiting time. Finally, we compute the minimal number of states the processors require to implement a single PIF cycle, and show that both algorithms for oriented trees are also (in addition to being time optimal) optimal in terms of the number of states.
A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In this paper, we present the first snap-stabilizing depth-first search wave protocol for ...
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A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In this paper, we present the first snap-stabilizing depth-first search wave protocol for arbitrary rooted networks assuming an unfair daemon, i.e. assuming the weakest scheduling assumption (a preliminary version of this work was presented in OPODIS 2004, 8th International Conference on Principles of Distributed Systems, Grenoble (France)).
A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behaves according to its specification. In other words, a snap-stabilizing protocol is a self-stabilizing protocol which st...
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A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behaves according to its specification. In other words, a snap-stabilizing protocol is a self-stabilizing protocol which stabilizes in zero steps. In this paper, we first prove the number of states required on processors to design a snap-stabilizing Propagation of Information with Feedback (PIF) algorithm in arbitrary un-oriented trees running under any distributed daemon (four states per processor for the middle processors and two states for each of the two extreme end processors). Then, we propose two snap-stabilizing PIF algorithms for un-oriented trees. The former works under any (fair or unfair, central or distributed) daemon. It matches the lower bound in terms of number of states we established in this paper. The latter works under any (fair or unfair) central daemon. It uses only three states for the internal processors (two states for the root and the leaves). It is optimal in terms of number of states assuming a central daemon. Thus, both algorithms are optimal both in terms of the stabilization time (zero steps) and state requirement per processor.
We present the first snap-stabilizing Propagation Of In formation with Feedback (PIF) protocol in arbitrary networks. A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behav...
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ISBN:
(纸本)0769515851
We present the first snap-stabilizing Propagation Of In formation with Feedback (PIF) protocol in arbitrary networks. A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behaves according to its specification. Our protocol is distributed, deterministic, and does not use a pre-constructed spanning tree.
We present a deterministic distributed Propagation of information with Feedback (PIF) protocol in arbitrary rooted networks. The proposed algorithm does not use a pre-constructed spanning tree. The protocol is self-st...
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ISBN:
(纸本)0769510779
We present a deterministic distributed Propagation of information with Feedback (PIF) protocol in arbitrary rooted networks. The proposed algorithm does not use a pre-constructed spanning tree. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to behave according to its specification. Every PIF wave initiated by the root inherently creates a tree in the graph. So, the tree is dynamically created according to the progress of the PIF wave. This allows our PIF algorithm to take advantage of the relative speed of different components of the network. The proposed algorithm can be easily used to implement any self-stabilizing system which requires a (self-stabilizing) wave protocol running on an arbitrary network.
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