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BACKGROUND: Semantic similarity searches in ontologies are an important component of many bioinformatic algorithms, e.g., finding functionally related proteins with the Gene Ontology or phenotypically similar diseases with the Human Phenotype Ontology (HPO). We have recently shown that the performance of semantic similarity searches can be improved by ranking results according to the probability of obtaining a given score at random rather than by the scores themselves. However, to date, there are no algorithms for computing the exact distribution of semantic similarity scores, which is necessary for computing the exact P-value of a given score. RESULTS: In this paper we consider the exact computation of score distributions for similarity searches in ontologies, and introduce a simple null hypothesis which can be used to compute a P-value for the statistical significance of similarity scores. We concentrate on measures based on Resnik's definition of ontological similarity. A new algorithm is proposed that collapses subgraphs of the ontology graph and thereby allows fast score distribution computation. The new algorithm is several orders of magnitude faster than the naive approach, as we demonstrate by computing score distributions for similarity searches in the HPO. It is shown that exact P-value calculation improves clinical diagnosis using the HPO compared to approaches based on sampling. CONCLUSIONS: The new algorithm enables for the first time exact P-value calculation via exact score distribution computation for ontology similarity searches. The approach is applicable to any ontology for which the annotation-propagation rule holds and can improve any bioinformatic method that makes only use of the raw similarity scores. The algorithm was implemented in Java, supports any ontology in OBO format, and is available for non-commercial and academic usage under: https://compbio.charite.de/svn/hpo/trunk/src/tools/significance/
