Maximal matching stabilizes in quadratic time

Tel, Gérard

doi:10.1016/0020-0190(94)90098-1

Cited by 32 publications

(23 citation statements)

References 1 publication

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“…Step complexity Round complexity [10,12,9] sequential adversarial O(m) [7] distributed adversarial finite [2] distributed fair…”

Section: Reference Daemonmentioning

confidence: 99%

“…Hsu and Huang [10] gave the first such algorithm and proved a bound of O(n 3 ) on the number of steps assuming an adversarial daemon. This analysis was later improved to O(n 2 ) by Tel [12] and finally to O(m) by Hedetniemi et al [9]. The original algorithm assumes an anonymous networks and operates therefore under the sequential daemon in order to achieve symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

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A New Self-stabilizing Maximal Matching Algorithm

Manne

Mjelde

Pilard

et al. 2007

Structural Information and Communication Complexity

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The maximal matching problem has received considerable attention in the selfstabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon, the sequential adversarial daemon, as well as the synchronous daemon. In the following we present a single self-stabilizing algorithm for this problem that unites all of these algorithms in that it stabilizes in the same number of moves as the previous best algorithms for the sequential adversarial, the distributed fair, and the synchronous daemon. In addition, the algorithm improves the previous best moves complexities for the distributed adversarial daemon from O(n 2 ) and O(δm) to O(m) where n is the number of processes, m is the number of edges, and δ is the maximum degree in the graph. Key-words:Distributed systems, Distributed algorithm, Self-stabilization, Maximal matching, Complexity * University of Bergen, Norway, {fredrikm,mortenm}@ii.uib

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“…Step complexity Round complexity [10,12,9] sequential adversarial O(m) [7] distributed adversarial finite [2] distributed fair…”

Section: Reference Daemonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Self-stabilizing Maximal Matching Algorithm

Manne

Mjelde

Pilard

et al. 2007

Structural Information and Communication Complexity

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show abstract

“…In [2] Tel shows that, in fact, the HsuHuang algorithm runs in O(n 2 ) time. More precisely, Tel shows that for any network having n nodes, the Hsu-Huang algorithm will stabilize within 1 2 n 2 + 2n + 1 moves.…”

Section: Introductionmentioning

confidence: 99%

“…For sparse networks such as trees, our result implies an O(n) bound. In both papers [1] and [2] a variant function is used for the complexity analysis. Our analysis uses a new proof technique that counts the number of moves that occur on a given edge.…”

Section: Introductionmentioning

confidence: 99%

Maximal matching stabilizes in time O(m)

Hedetniemi

Jacobs

Srimani

2001

Information Processing Letters

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“…In [2], Hsu and Huang show that it is bounded by O(n 3 ), where n is the number of nodes. In [3], Tel provides an almost tight upper bound, which is 1 2 n 2 +2n+1 if n is even and 1 2 n 2 +n− 1 2 if n is odd. In [4] Tel gives a more concise proof for the O(n 2 ) bound than [3].…”

Section: Introductionmentioning

confidence: 99%