Can we elect if we cannot compare?

  • Authors:

  • Lali Barrière;Paola Flocchin;Pierre Fraigniau;Nicola Santor

  • Affiliations:

  • Universita Politècnica de Catalunya, Barcelona, Spain;University of Ottawa, Ottawa, Canada;Université Paris Sud, Orsay, France;Carleton University, Ottawa, Canada

  • Venue:
  • Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
  • Year:
  • 2003

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Abstract

The aim of this paper is to study the computational power of the qualitative model, where entities are given distinct labels which are however mutually incomparable; this model is opposed to the quantitative model, where labels are integers. The qualitative model captures, for example,the case when the labels are written in different alphabets (e.g., Cyrillic, Latin) and there is no a priori agreement on a common encoding. We investigate the qualitative model through the problem of leader election in a distributed mobile environment. All known leader election protocols assume that the initial input values are distinct and pairwise comparable. While distinctness of the input values is clearly required, the comparability assumption is questionable. Our concern is whether it is possible to remove this comparability assumption. To focus solely on this concern, we consider theproblem in its weakest setting: anonymous highly symmetric networks (i.e.,Cayley graphs). In this way, to break the symmetry (and thus elect a leader) among the incomparable mobile agents, we can not rely on the existence of distinguished node labels nor on any topological asymmetry of the network. We describe a generic election protocol which is effective for all anonymous Cayley graphs; i.e., it solves the election problem if the problem is solvable, otherwise it determines that the problem is not solvable. For arbitrary networks, our protocol is conditionally effective; that is, it performs election of one agent among any set of agents in any network, under some weak conditions on the network and on the initial positions of the agents. Our work is a first step toward a better understanding of the inherent differences between "quantitative computing" where parameters are taken from a total order, and "qualitative computing" where parameters are taken from a partial order.