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Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms
[article]

2021
*
arXiv
*
pre-print

In addition, we show that our

arXiv:1905.08563v3
fatcat:wctfkduvevgi5j4zwdfpwq77km
*lower**bounds*go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms. ... .), a*self*-*stabilizing*algorithm*for*Π is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables ... Any*lower**bound*on the size of the proofs in a PLS*for*a predicate Π on labeled graph implies a*lower**bound*on the size of the registers*for*silent*self*-*stabilizing*algorithms solving Π. ...##
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Brief Announcement: Memory Lower Bounds for Self-Stabilization

2019
*
International Symposium on Distributed Computing
*

We improve this result by establishing the

doi:10.4230/lipics.disc.2019.37
dblp:conf/wdag/BlinFB19
fatcat:ucwvrbj4xfflhje6sk65f7ksde
*lower**bound*Ω(log log n) bits per register*for*deterministic*self*-*stabilizing*algorithms solving (∆ + 1)-coloring, leader election or constructing a spanning ... To our knowledge, the only known*lower**bound*on the*memory*requirement*for*deterministic general algorithms, also established at the end of the 90's, is due to Beauquier et al. ...*Memory**Lower**Bounds**for**Self*-*Stabilization*In the state model, the processes have two types of*memory*. ...##
###
Brief announcement

2013
*
Proceedings of the 2013 ACM symposium on Principles of distributed computing - PODC '13
*

This

doi:10.1145/2484239.2484289
dblp:conf/podc/BlinT13
fatcat:b3ehjxpzs5gbtooym6m5xugkam
*lower**bound*holds even in rings. ... We present a new deterministic (non-silent)*self*-*stabilizing*protocol*for*n-node rings that uses only O(log log n)*memory*bits per node, and*stabilizes*in O(n log 2 n) time. ... A few previous works [24, 21, 5, 22] managed to break the Ω(log n) bits*lower**bound**for*the*memory*space of selfstabilizing leader election algorithms. ...##
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Self-stabilizing Java

2012
*
SIGPLAN notices
*

We present a type system and static analyses that together check whether a program is

doi:10.1145/2345156.2254099
fatcat:e5tsormidzcr7g7x5wryjqrim4
*self*-*stabilizing*. ...*Self*-*stabilizing*programs automatically recover from state corruption caused by software bugs and other sources to reach the correct state. ... We would like to thank Patrick Lam, Harry Xu, Philip Reames, Philippe Suter, and the anonymous reviewers*for*their helpful comments. We would like to thank James Jenista*for*help with the experiments. ...##
###
Self-stabilizing Java

2012
*
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation - PLDI '12
*

We present a type system and static analyses that together check whether a program is

doi:10.1145/2254064.2254099
dblp:conf/pldi/EomD12
fatcat:b5xvl6pvkjduxetzx4kdc6j5ei
*self*-*stabilizing*. ...*Self*-*stabilizing*programs automatically recover from state corruption caused by software bugs and other sources to reach the correct state. ... We would like to thank Patrick Lam, Harry Xu, Philip Reames, Philippe Suter, and the anonymous reviewers*for*their helpful comments. We would like to thank James Jenista*for*help with the experiments. ...##
###
Local Algorithms: Self-stabilization on Speed
[chapter]

2009
*
Lecture Notes in Computer Science
*

Such

doi:10.1007/978-3-642-05118-0_2
fatcat:tp3fdm4hzvcjdjgbqxbeuaqwmy
*lower**bounds*have applications far beyond linear programming, as they also give*lower**bounds**for*the original combinatorial problems. ... Most of the results are deterministic algorithms or*lower*-*bound*results, each of which has a direct*self*-*stabilizing*counterpart. ...##
###
Self-stabilizing Graph Exploration by a Single Agent
[article]

2020
*
arXiv
*
pre-print

It uses O(log n) bits

arXiv:2010.08929v1
fatcat:5sql46kupzdkpolngzq6zgq4gq
*for*the agent-*memory*and O(δ + log n) bits*for*the*memory*of each node with degree δ. We require the knowledge of an upper*bound*on n (resp. ... In this paper, we give two*self*-*stabilizing*algorithms that solve graph exploration by a single (mobile) agent. ... (*For*completeness, we will prove this*lower**bound*in Section 5.) ...##
###
Compact Deterministic Self-stabilizing Leader Election
[chapter]

2013
*
Lecture Notes in Computer Science
*

This

doi:10.1007/978-3-642-41527-2_6
fatcat:uelkodsrjzd2fmclrnl2lspd5m
*lower**bound*holds even in rings. ... We present a new deterministic (non-silent)*self*-*stabilizing*protocol*for*n-node rings that uses only O(log log n)*memory*bits per node, and*stabilizes*in O(n log 2 n) time. ... A few previous work [27, 24, 6, 25] managed to break the Ω(log n) bits*lower**bound**for*the*memory*space of*self*-*stabilizing*leader election algorithms. ...##
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OCD

2008
*
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing - PODC '08
*

*For*systems with multi-value inputs, we show that the output may change at most twice; when n = 3f + 1 this solution is shown to be tight. Moreover, the solutions we present are

*self*-

*stabilizing*. ... We show that any system with binary input values can avoid changing its output more than once, thus matching the

*lower*

*bound*. ... Acknowledgements We would like to thank Yoni Peleg

*for*contributing Theorem 5. ...

##
###
Building Self-stabilizing Overlay Networks with the Transitive Closure Framework
[chapter]

2011
*
Lecture Notes in Computer Science
*

a

doi:10.1007/978-3-642-24550-3_7
fatcat:34oi5wnxojgntdwthrqls2prdi
*memory*-efficient fashion. ... runs in an optimal number of rounds*for*a variety of overlay networks, and (iii) it can easily be composed with other non-*self*-*stabilizing*protocols that can recover from specific bad initial states in ... To place this in context, we then show a*lower**bound*: the worst-case*self*-*stabilization*time of an algorithm derived from TCF is*bounded*below by Ω(Diam(G)). ...##
###
Building self-stabilizing overlay networks with the transitive closure framework

2013
*
Theoretical Computer Science
*

a

doi:10.1016/j.tcs.2013.02.021
fatcat:mb2w6ywbkvdqdbfyfqrqxulxli
*memory*-efficient fashion. ... runs in an optimal number of rounds*for*a variety of overlay networks, and (iii) it can easily be composed with other non-*self*-*stabilizing*protocols that can recover from specific bad initial states in ... To place this in context, we then show a*lower**bound*: the worst-case*self*-*stabilization*time of an algorithm derived from TCF is*bounded*below by Ω(Diam(G)). ...##
###
Optimal deterministic self-stabilizing vertex coloring in unidirectional anonymous networks

2009
*
2009 IEEE International Symposium on Parallel & Distributed Processing
*

Specifically, we prove a

doi:10.1109/ipdps.2009.5161053
dblp:conf/ipps/BernardDPT09
fatcat:6v5vrjop6ncqnd6rbtmqfktwcm
*lower**bound*of n states per process (where n is the network size) and a recovery time of at least n(n−1)/2 actions in total. ... Unidirectional networks preclude many common techniques in*self*-*stabilization*from being used, such as preserving local predicates. ... .). [12] provides a time*lower**bound**for**self*-*stabilizing*token passing, still a global task. ...##
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Resource bounds for self stabilizing message driven protocols

1991
*
Proceedings of the tenth annual ACM symposium on Principles of distributed computing - PODC '91
*

Then we present three

doi:10.1145/112600.112624
dblp:conf/podc/DolevIM91
fatcat:6aemtyqkz5hepjvss3uosxn6ny
*self*-*stabilizing*message driven protocols*for*token-passing. The rate of growth of configuration size*for*all three protocols matches the aforementioned*lower**bound*. ...*Self*-*stabilizing*message driven protocols are defined and discussed. ... We thank Alan Fekete*for*helpful remarks. ...##
###
Resource Bounds for Self-Stabilizing Message-Driven Protocols

1997
*
SIAM journal on computing (Print)
*

Then we present three

doi:10.1137/s0097539792235074
fatcat:6ypcyzxavvat3jvv332hl7cv7y
*self*-*stabilizing*message driven protocols*for*token-passing. The rate of growth of configuration size*for*all three protocols matches the aforementioned*lower**bound*. ...*Self*-*stabilizing*message driven protocols are defined and discussed. ... We thank Alan Fekete*for*helpful remarks. ...##
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Fast and compact self stabilizing verification, computation, and fault detection of an MST

2011
*
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '11
*

When used

doi:10.1145/1993806.1993866
dblp:conf/podc/KormanKM11
fatcat:45cvoliscrhatolo2h5rhgqlna
*for*MST, the transformer produces a*memory*optimal (i.e., O(log n) bits per node)*self**stabilizing*algo- * rithm, whose time complexity, namely, O(n), is significantly better even than that of ... It now takes as input an efficient construction algorithm and an efficient*self**stabilizing*proof labeling scheme, and produces an efficient*self**stabilizing*algorithm. ... This includes,*for*example, the logarithmic time*lower**bound*. ...
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