A self‐stabilizing distributed algorithm for the local (1,|Ni|)‐critical section problem

Summary We consider the local (1,|Ni|)‐critical section (CS) problem where Ni is the set of neighboring processes for each process Pi. It dynamically maintains two disjoint dominating sets and is one of the generalizations of the mutual exclusion problem. The problem is one of controlling the system...

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Vydáno v:Concurrency and computation Ročník 33; číslo 12
Hlavní autoři: Kamei, Sayaka, Kakugawa, Hirotsugu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken Wiley Subscription Services, Inc 25.06.2021
Témata:
Algorithms
disjoint minimal dominating sets
domatic partition
Matching
mutual exclusion
mutual inclusion
Scheduling
self‐stabilization
ISSN:1532-0626, 1532-0634
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Shrnutí:Summary We consider the local (1,|Ni|)‐critical section (CS) problem where Ni is the set of neighboring processes for each process Pi. It dynamically maintains two disjoint dominating sets and is one of the generalizations of the mutual exclusion problem. The problem is one of controlling the system in such a way that, for each process, among its neighbors and itself, at least one process must be in the CS and at least one process must be out of the CS at each time. That is, in the system G=(V,E), there are always two disjoint dominating sets A1(⊂V) and A2(=V\A1) and each process alternates between its rule A1 and A2 infinitely. It is useful for sleep scheduling or cluster head scheduling in sensor networks. In this paper, first, we show the necessary and sufficient conditions to solve the problem without any deadlock detection. To discuss the conditions, we consider an inefficient (costly) self‐stabilizing algorithm for the local (1,|Ni|)‐CS problem. After that, an efficient self‐stabilizing algorithm for the local (1,|Ni|)‐CS problem is proposed under an additional assumption that the graph does not have a special matching, which we call unpreventable colorable maximal matching. The convergence time of the proposed algorithm is O(n) rounds under the weakly fair distributed daemon.
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ISSN:1532-0626
1532-0634
DOI:10.1002/cpe.5628