Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Abstract In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in settings queries asked sequentially (adaptive model) or all at once (non-adaptive model). We introduce a new model k made parallel each round, and goal is to minimize number rounds. Using competitive analysis, we present upper lower bounds on rounds required by any algorithm comparison optimal for given instance. Given set uncertain family m subsets that set, study sorting determining minimum value (or element(s)) subset. also selection problem, i.e., problem i -th smallest identifying elements. Our results include 2-round-competitive algorithms an uses most $$(2+\varepsilon ) \cdot \mathrm {opt}_k+\mathrm {O}\left( \frac{1}{\varepsilon } \lg m\right) $$ ( 2 + ε ) · opt k O 1 lg m every $$0<\varepsilon <1$$ 0 < , $$\mathrm {opt}_k$$