An Improved Deterministic Algorithm for the Online Min-Sum Set Cover Problem
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We study the online variant of the Min-Sum Set Cover (MSSC) problem, a generalization of the well-known list update problem. In the MSSC problem, an algorithm has to maintain the time-varying permutation of the list of n elements, and serve a sequence of requests R_1, R_2, …, R_t, …. Each R_t is a subset of elements of cardinality at most r. For a requested set R_t, an online algorithm has to pay the cost equal to the position of the first element from R_t on its list. Then, it may arbitrarily permute its list, paying the number of swapped adjacent element pairs. We present the first constructive deterministic algorithm for this problem, whose competitive ratio does not depend on n. Our algorithm is O(r^2)-competitive, which beats both the existential upper bound of O(r^4) by Bienkowski and Mucha [AAAI '23] and the previous constructive bound of O(r^3/2·√(n)) by Fotakis et al. [ICALP '20]. Furthermore, we show that our algorithm attains an asymptotically optimal competitive ratio of O(r) when compared to the best fixed permutation of elements.
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