TY - CHAP

T1 - On proof-labeling schemes versus silent self-stabilizing algorithms

AU - Blin, Lélia

AU - Fraigniaud, Pierre

AU - Patt-Shamir, Boaz

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.

PY - 2014

Y1 - 2014

N2 - It follows from the definition of silent self-stabilization, and from the definition of proof-labeling scheme, that if there exists a silent self-stabilizing algorithm using l-bit registers for solving a task T, then there exists a proof-labeling scheme for T using registers of at most l bits. The first result in this paper is the converse to this statement. We show that if there exists a proof-labeling scheme for a task T, using l-bit registers, then there exists a silent self-stabilizing algorithm using registers of at most O(l + log n) bits for solving T, where n is the number of processes in the system. Therefore, as far as memory space is concerned, the design of silent self-stabilizing algorithms essentially boils down to the design of compact proof-labeling schemes. The second result in this paper addresses time complexity. We show that, for every task T with k-bits output size in n-node networks, there exists a silent self-stabilizing algorithm solving T in O(n) rounds, using registers of O(n2 + kn) bits. Therefore, as far as running time is concerned, every task has a silent self-stabilizing algorithm converging in a linear number of rounds.

AB - It follows from the definition of silent self-stabilization, and from the definition of proof-labeling scheme, that if there exists a silent self-stabilizing algorithm using l-bit registers for solving a task T, then there exists a proof-labeling scheme for T using registers of at most l bits. The first result in this paper is the converse to this statement. We show that if there exists a proof-labeling scheme for a task T, using l-bit registers, then there exists a silent self-stabilizing algorithm using registers of at most O(l + log n) bits for solving T, where n is the number of processes in the system. Therefore, as far as memory space is concerned, the design of silent self-stabilizing algorithms essentially boils down to the design of compact proof-labeling schemes. The second result in this paper addresses time complexity. We show that, for every task T with k-bits output size in n-node networks, there exists a silent self-stabilizing algorithm solving T in O(n) rounds, using registers of O(n2 + kn) bits. Therefore, as far as running time is concerned, every task has a silent self-stabilizing algorithm converging in a linear number of rounds.

UR - http://www.scopus.com/inward/record.url?scp=84908299240&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-11764-5_2

DO - 10.1007/978-3-319-11764-5_2

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AN - SCOPUS:84908299240

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 18

EP - 32

BT - Stabilization, Safety and Security of Distributed Systems

A2 - Felber, Pascal

A2 - Garg, Vijay K.

PB - Springer Verlag

ER -