Approximation Guarantees for Max Sum and Max Min Facility Dispersion with Parameterised Triangle Inequality and Applications in Result Diversification

Facility Dispersion Problem, originally studied in Operations Research, recently found important new applications in Result Diversification approach in sciences. This optimisation problem consists of selecting a small set of items out of a large set of candidates to maximise a given objective function. The expresses the notion of dispersion of a set of selected items in terms of a -wise distance measure between items. most known formulations the problem is NP-hard, but there exist 2-approximation for some cases if distance satisfies triangle inequality. present generalised 2/α approximation guarantees for the Facility Dispersion in its two most common variants: Max Sum and Max Min, when the un- dissimilarity measure satisfies parameterised triangle inequality with pa- α. The results apply to both relaxed and stronger variants of the triangle . also demonstrate potential applications of our findings in the result diversifica- problem including web search or entity summarisation in semantic knowledge , as well as in practical computations on finite data sets.