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Algorithms to solve hard combinatorial problems often exhibit complementary performance, i.e. where one algorithm fails, another shines. Algorithm portfolios and algorithm selection take advantage of this by running all algorithms in parallel or choosing the best one to run on a problem instance. In this paper, we show that neither of these approaches gives the best possible performance and propose the happy medium of running a subset of all algorithms in parallel. We propose a method to choose this subset automatically for each problem instance, and demonstrate empirical improvements of up to 19% in terms of runtime, 81% in terms of misclassification penalty, and 26% in terms of penalized averaged runtime on scenarios from the ASlib benchmark library. Unlike all other algorithm selection and scheduling approaches in the literature, our performance measures are based on the actual performance for algorithms running in parallel rather than assuming overhead-free parallelization based on sequential performance. Our approach is easy to apply in practice and does not require to solve hard problems to obtain a schedule, unlike other techniques in the literature, while still delivering superior performance.
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