Snap-stabilization and PIF in tree networks

Abstract 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...
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Autor*in:	Bui, Alain [verfasserIn] Datta, Ajoy K. Petit, Franck Villain, Vincent

Format:	Artikel
Sprache:	Englisch

Erschienen:	2007

Schlagwörter:	Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms

Anmerkung:	© Springer-Verlag 2007

Übergeordnetes Werk:	Enthalten in: Distributed computing - Springer-Verlag, 1986, 20(2007), 1 vom: Juli, Seite 3-19
Übergeordnetes Werk:	volume:20 ; year:2007 ; number:1 ; month:07 ; pages:3-19

Links:	Volltext

DOI / URN:	10.1007/s00446-007-0030-4

Katalog-ID:	OLC2054809438

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520			\|a Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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.
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allfields	10.1007/s00446-007-0030-4 doi (DE-627)OLC2054809438 (DE-He213)s00446-007-0030-4-p DE-627 ger DE-627 rakwb eng 004 VZ 620 VZ Bui, Alain verfasserin aut Snap-stabilization and PIF in tree networks 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms Datta, Ajoy K. aut Petit, Franck aut Villain, Vincent aut Enthalten in Distributed computing Springer-Verlag, 1986 20(2007), 1 vom: Juli, Seite 3-19 (DE-627)13042885X (DE-600)635600-X (DE-576)01592789X 0178-2770 nnns volume:20 year:2007 number:1 month:07 pages:3-19 https://doi.org/10.1007/s00446-007-0030-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2244 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4318 GBV_ILN_4319 AR 20 2007 1 07 3-19
spelling	10.1007/s00446-007-0030-4 doi (DE-627)OLC2054809438 (DE-He213)s00446-007-0030-4-p DE-627 ger DE-627 rakwb eng 004 VZ 620 VZ Bui, Alain verfasserin aut Snap-stabilization and PIF in tree networks 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms Datta, Ajoy K. aut Petit, Franck aut Villain, Vincent aut Enthalten in Distributed computing Springer-Verlag, 1986 20(2007), 1 vom: Juli, Seite 3-19 (DE-627)13042885X (DE-600)635600-X (DE-576)01592789X 0178-2770 nnns volume:20 year:2007 number:1 month:07 pages:3-19 https://doi.org/10.1007/s00446-007-0030-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2244 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4318 GBV_ILN_4319 AR 20 2007 1 07 3-19
allfields_unstemmed	10.1007/s00446-007-0030-4 doi (DE-627)OLC2054809438 (DE-He213)s00446-007-0030-4-p DE-627 ger DE-627 rakwb eng 004 VZ 620 VZ Bui, Alain verfasserin aut Snap-stabilization and PIF in tree networks 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms Datta, Ajoy K. aut Petit, Franck aut Villain, Vincent aut Enthalten in Distributed computing Springer-Verlag, 1986 20(2007), 1 vom: Juli, Seite 3-19 (DE-627)13042885X (DE-600)635600-X (DE-576)01592789X 0178-2770 nnns volume:20 year:2007 number:1 month:07 pages:3-19 https://doi.org/10.1007/s00446-007-0030-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2244 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4318 GBV_ILN_4319 AR 20 2007 1 07 3-19
allfieldsGer	10.1007/s00446-007-0030-4 doi (DE-627)OLC2054809438 (DE-He213)s00446-007-0030-4-p DE-627 ger DE-627 rakwb eng 004 VZ 620 VZ Bui, Alain verfasserin aut Snap-stabilization and PIF in tree networks 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms Datta, Ajoy K. aut Petit, Franck aut Villain, Vincent aut Enthalten in Distributed computing Springer-Verlag, 1986 20(2007), 1 vom: Juli, Seite 3-19 (DE-627)13042885X (DE-600)635600-X (DE-576)01592789X 0178-2770 nnns volume:20 year:2007 number:1 month:07 pages:3-19 https://doi.org/10.1007/s00446-007-0030-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2244 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4318 GBV_ILN_4319 AR 20 2007 1 07 3-19
allfieldsSound	10.1007/s00446-007-0030-4 doi (DE-627)OLC2054809438 (DE-He213)s00446-007-0030-4-p DE-627 ger DE-627 rakwb eng 004 VZ 620 VZ Bui, Alain verfasserin aut Snap-stabilization and PIF in tree networks 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms Datta, Ajoy K. aut Petit, Franck aut Villain, Vincent aut Enthalten in Distributed computing Springer-Verlag, 1986 20(2007), 1 vom: Juli, Seite 3-19 (DE-627)13042885X (DE-600)635600-X (DE-576)01592789X 0178-2770 nnns volume:20 year:2007 number:1 month:07 pages:3-19 https://doi.org/10.1007/s00446-007-0030-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2244 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4318 GBV_ILN_4319 AR 20 2007 1 07 3-19
language	English
source	Enthalten in Distributed computing 20(2007), 1 vom: Juli, Seite 3-19 volume:20 year:2007 number:1 month:07 pages:3-19
sourceStr	Enthalten in Distributed computing 20(2007), 1 vom: Juli, Seite 3-19 volume:20 year:2007 number:1 month:07 pages:3-19
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Fault-tolerance Optimality Self-stabilization Snap-stabilization Wave algorithms
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isfreeaccess_bool	false
container_title	Distributed computing
authorswithroles_txt_mv	Bui, Alain @@aut@@ Datta, Ajoy K. @@aut@@ Petit, Franck @@aut@@ Villain, Vincent @@aut@@
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author	Bui, Alain
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title	Snap-stabilization and PIF in tree networks
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title_full	Snap-stabilization and PIF in tree networks
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title_sort	snap-stabilization and pif in tree networks
title_auth	Snap-stabilization and PIF in tree networks
abstract	Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. © Springer-Verlag 2007
abstractGer	Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. © Springer-Verlag 2007
abstract_unstemmed	Abstract 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 ($$\mathcal{PFC}$$). We show three different implementations of this new PIF. The first one is a basic $$\mathcal{PFC}$$ cycle which is inherently snap-stabilizing. However, the first PIF cycle can be delayed O(h2) 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 $$\mathcal{PFC}$$ algorithm from O(h2) 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. © Springer-Verlag 2007
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title_short	Snap-stabilization and PIF in tree networks
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