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

Lélia Blin, Laurent Feuilloley, Gabriel Le Bouder
2021 arXiv   pre-print
In addition, we show that our 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.  ... 
arXiv:1905.08563v3 fatcat:wctfkduvevgi5j4zwdfpwq77km

Brief Announcement: Memory Lower Bounds for Self-Stabilization

Lélia Blin, Laurent Feuilloley, Gabriel Le Bouder, Michael Wagner
2019 International Symposium on Distributed Computing  
We improve this result by establishing the 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.  ... 
doi:10.4230/lipics.disc.2019.37 dblp:conf/wdag/BlinFB19 fatcat:ucwvrbj4xfflhje6sk65f7ksde

Brief announcement

Lélia Blin, Sébastien Tixeuil
2013 Proceedings of the 2013 ACM symposium on Principles of distributed computing - PODC '13  
This 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.  ... 
doi:10.1145/2484239.2484289 dblp:conf/podc/BlinT13 fatcat:b3ehjxpzs5gbtooym6m5xugkam

Self-stabilizing Java

Yong hun Eom, Brian Demsky
2012 SIGPLAN notices  
We present a type system and static analyses that together check whether a program is 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.  ... 
doi:10.1145/2345156.2254099 fatcat:e5tsormidzcr7g7x5wryjqrim4

Self-stabilizing Java

Yong hun Eom, Brian Demsky
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 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.  ... 
doi:10.1145/2254064.2254099 dblp:conf/pldi/EomD12 fatcat:b5xvl6pvkjduxetzx4kdc6j5ei

Local Algorithms: Self-stabilization on Speed [chapter]

Christoph Lenzen, Jukka Suomela, Roger Wattenhofer
2009 Lecture Notes in Computer Science  
Such 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.  ... 
doi:10.1007/978-3-642-05118-0_2 fatcat:tp3fdm4hzvcjdjgbqxbeuaqwmy

Self-stabilizing Graph Exploration by a Single Agent [article]

Yuichi Sudo, Fukuhito Ooshita, Sayaka Kamei
2020 arXiv   pre-print
It uses O(log n) bits 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.)  ... 
arXiv:2010.08929v1 fatcat:5sql46kupzdkpolngzq6zgq4gq

Compact Deterministic Self-stabilizing Leader Election [chapter]

Lélia Blin, Sébastien Tixeuil
2013 Lecture Notes in Computer Science  
This 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.  ... 
doi:10.1007/978-3-642-41527-2_6 fatcat:uelkodsrjzd2fmclrnl2lspd5m

OCD

Danny Dolev, Ezra N. Hoch
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.  ... 
doi:10.1145/1400751.1400803 dblp:conf/podc/DolevH08 fatcat:o65vzdzu75h3vazrizgiywuiy4

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

Andrew Berns, Sukumar Ghosh, Sriram V. Pemmaraju
2011 Lecture Notes in Computer Science  
a 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)).  ... 
doi:10.1007/978-3-642-24550-3_7 fatcat:34oi5wnxojgntdwthrqls2prdi

Building self-stabilizing overlay networks with the transitive closure framework

Andrew Berns, Sukumar Ghosh, Sriram V. Pemmaraju
2013 Theoretical Computer Science  
a 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)).  ... 
doi:10.1016/j.tcs.2013.02.021 fatcat:mb2w6ywbkvdqdbfyfqrqxulxli

Optimal deterministic self-stabilizing vertex coloring in unidirectional anonymous networks

Samuel Bernard, Stephane Devismes, Maria Gradinariu Potop-Butucaru, Sebastien Tixeuil
2009 2009 IEEE International Symposium on Parallel & Distributed Processing  
Specifically, we prove a 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.  ... 
doi:10.1109/ipdps.2009.5161053 dblp:conf/ipps/BernardDPT09 fatcat:6v5vrjop6ncqnd6rbtmqfktwcm

Resource bounds for self stabilizing message driven protocols

Shlomi Dolev, Amos Israeli, Shlomo Moran
1991 Proceedings of the tenth annual ACM symposium on Principles of distributed computing - PODC '91  
Then we present three 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.  ... 
doi:10.1145/112600.112624 dblp:conf/podc/DolevIM91 fatcat:6aemtyqkz5hepjvss3uosxn6ny

Resource Bounds for Self-Stabilizing Message-Driven Protocols

Shlomi Dolev, Amos Israeli, Shlomo Moran
1997 SIAM journal on computing (Print)  
Then we present three 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.  ... 
doi:10.1137/s0097539792235074 fatcat:6ypcyzxavvat3jvv332hl7cv7y

Fast and compact self stabilizing verification, computation, and fault detection of an MST

Amos Korman, Shay Kutten, Toshimitsu Masuzawa
2011 Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '11  
When used 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.  ... 
doi:10.1145/1993806.1993866 dblp:conf/podc/KormanKM11 fatcat:45cvoliscrhatolo2h5rhgqlna
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