The vast majority of work on skyline queries considers totally ordered domains, whereas in many applications some attributes are partially ordered, as for instance, domains of set values, hierarchies, intervals and preferences. The only work addressing this issue has limited progressiveness and pruning ability, and it is only applicable to static skylines. This paper overcomes these problems with the following contributions. (i) We introduce a generic framework, termed TSS, for handling partially ordered domains using topological sorting. (ii) We propose a novel dominance check that eliminates false hits/misses, further enhancing progressiveness and pruning ability. (iii) We extend our methodology to dynamic skylines with respect to an input query. In this case, the dominance relationships change according to the query specification, and their computation is rather complex. We perform an extensive experimental evaluation demonstrating that TSS is up to 9 times and up to 2 orders of magnitude faster than existing methods in the static and the dynamic case, respectively.
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