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Locally Derivable Graphs

100%

Mazurkiewicz A.

tom Vol. 75, nr 1-4

335-355

In the paper a class of locally derivable graphs is defined and discussed. Well known particular cases of derivable graphs are (among others) trees, complete, and triangular graphs; in the paper a broader class of locally derivable graphs, called closed graphs, is defined. Nodes and edges of closed graphs can be partitioned into external and internal ones; the main property of such graphs their local reducibility: successive removing its external nodes leads eventually to a singleton, and removing its external edges leads to an a spanning tree of the graph. The class of closed graphs is then a class enabling structural reducing. This property can be applied in processor networks to design some local procedures leading to global results.

Local Computations in Graphs: The Case of Cellular Edge Local Computations

88%

Chalopin J. , Métivier Y. , Zielonka W.

tom Vol. 74, nr 1

85-114

We examine the power and limitations of the weakest vertex relabelling system which allows to change a label of a vertex in function of its own label and of the label of one of its neighbours. We characterize the graphs for which two important distributed algorithmic problems are solvable in this model : naming and election.

An Efficient Message Passing Election Algorithm based on Mazurkiewicz's Algorithm

75%

Chalopin J. , Métivier Y.

2007

tom Vol. 80, nr 1-3

221-246

We study the election and the naming problems in the asynchronous message passing model. We present a necessary condition based on Angluin's lifting lemma [1] that must be satisfied by any network that admits a naming (or an election) algorithm. We then show that this necessary condition is also sufficient: we present an election and naming algorithm based on Mazurkiewicz's algorithm [17]. The algorithm we obtained is totally asynchronous and it needs a polynomial number of messages of polynomial size, whereas previous election algorithms in this model are pseudo-synchronous and use messages of exponential size.