Approximate algorithms for solving O 1 consensus problems using complex tree structure

Abstract

The consensus finding problem is known in the literature as a solution to inconsistency problems. Such inconsistency may come from different opinions of problem participants or data uncertainty. Consensus methods are used to find elements that represent all others in the inconsistent dataset and are a good compromise of the differing opinions. The O 1 solution to consensus problem is best defined as finding the element that has the smallest sum of distances to all other elements. It is solved for many simple structures, but not for the complex tree structure. In this paper we propose several algorithms to find O 1 consensus for complex trees (extended labeled trees), including a greedy algorithm and several approximate algorithms. We evaluate their approximation levels in terms of the 1-optimality criterion. © 2012 Springer-Verlag.