Leader Election in Abelian Cayley Graphs
نویسندگان
چکیده
In this paper we consider the problem of distributed leader election in unoriented Abelian Cayley graphs of degree 4. This family of graphs, denoted by C G 4, include bidimensional tori of arbitrary size and chordal rings with one arbitrary chord. We present an algorithm which assumes that the only structural knowledge available to the nodes is “I am in an Abelian Cayley Graph of degree 4”. The message complexity of our algorithm, for a graph of C G 4 of order N and diameter D, is O(N +D log D2 N ). The obliviousness of our algorithm to the underlying topology has been achieved by studying the properties of tessellations of the plane and reducing the problem of leader election in a graph from C G 4 to election in the associated tessellation.
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