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