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Structure of Initial Conditions for Distributed Algorithms

Naoshi SAKAMOTO

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Summary :

We call a network an anonymous network, if each vertex of the network is given no ID's. For distributed algorithms for anonymous networks, solvable problems depend strongly on the given initial conditions. In the past, initial conditions have been investigated, for example, by computation given the number of vertices as the initial condition, and in terms of what initial condition is needed to elect a leader. In this paper, we study the relations among initial conditions. To achieve this task, we define the relation between initial conditions A and B (denoted by A B) as the relation that some distributed algorithm can compute B on any network satisfying A. Then we show the following property of this relation among initial conditions. The relation is a partial order with respect to equivalence classes. Moreover, over initial conditions, it induces a lattice which has maxima and minima, and contains an infinite number of elements. On the other hand, we give new initial conditions k-LEADER and k-COLOR. k-LEADER denotes the initial condition that gives special condition only to k vertices. k-COLOR denotes the initial condition that divides the vertices into k groups. Then we investigate the property of the relation among these initial conditions.

Publication
IEICE TRANSACTIONS on Information Vol.E83-D No.12 pp.2029-2038
Publication Date
2000/12/25
Publicized
Online ISSN
DOI
Type of Manuscript
Special Section INVITED PAPER (Special Issue on the 1999 IEICE Excellent Paper Award)
Category
Theory and Models of Software

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