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A very computationally-efficient Monte-Carlo algorithm for the calculation ofDempster-Shafer belief is described. If Bel is the combination using Dempster'sRule of belief functions Bel, ..., Bel,7, then, for subset b of the frame C),Bel(b) can be calculated in time linear in 1(31 and m (given that the weight ofconflict is bounded). The algorithm can also be used to improve the complexityof the Shenoy-Shafer algorithms on Markov trees, and be generalised tocalculate Dempster-Shafer Belief over other logics.

A Monte-Carlo Algorithm for Dempster-Shafer Belief