Computational Aspects of the Möbius Transformation
Robert Kennes, Philippe Smets
In this paper we associate with every (directed) graph G a transformation called the Mobius transformation of the graph G. The Mobius transformation of the graph (O) is of major significance for Dempster-Shafer theory of evidence. However, because it is computationally very heavy, the Mobius transformation together with Dempster's rule of combination is a major obstacle to the use of Dempster-Shafer theory for handling uncertainty in expert systems. The major contribution of this paper is the discovery of the 'fast Mobius transformations' of (O). These 'fast Mobius transformations' are the fastest algorithms for computing the Mobius transformation of (O). As an easy but useful application, we provide, via the commonality function, an algorithm for computing Dempster's rule of combination which is much faster than the usual one.
PDF Link: /papers/90/p401-kennes.pdf
AUTHOR = "Robert Kennes
and Philippe Smets",
TITLE = "Computational Aspects of the Möbius Transformation",
BOOKTITLE = "Uncertainty in Artificial Intelligence 6 Annual Conference on Uncertainty in Artificial Intelligence (UAI-90)",
PUBLISHER = "Elsevier Science",
ADDRESS = "Amsterdam, NL",
YEAR = "1990",
PAGES = "401--416"