# The Online Min-Sum Set Cover Problem

@article{Fotakis2020TheOM,
title={The Online Min-Sum Set Cover Problem},
author={D. Fotakis and L. Kavouras and G. Koumoutsos and Stratis Skoulakis and Manolis Vardas},
journal={ArXiv},
year={2020},
volume={abs/2003.02161}
}
We consider the online Min-Sum Set Cover (MSSC), a natural and intriguing generalization of the classical list update problem. In Online MSSC, the algorithm maintains a permutation on $n$ elements based on subsets $S_1, S_2, \ldots$ arriving online. The algorithm serves each set $S_t$ upon arrival, using its current permutation $\pi_{t}$, incurring an access cost equal to the position of the first element of $S_t$ in $\pi_{t}$. Then, the algorithm may update its permutation to $\pi_{t+1… Expand 3 Citations Efficient Online Learning of Optimal Rankings: Dimensionality Reduction via Gradient Descent • Computer Science • NeurIPS • 2020 This work shows how to achieve low regret for GMSSC in polynomial-time by employing dimensionality reduction from rankings to the space of doubly stochastic matrices, where it is shown how subgradients can be computed efficiently, by solving the dual of a configuration LP. Expand On the Approximability of Multistage Min-Sum Set Cover • Computer Science • ICALP • 2021 The polynomial-time approximability of the multistage version of Min-Sum Set Cover (Mult-MSSC), a natural and intriguing generalization of the classical List Update problem, can be approximated within a factor of O(log2 n) in general instances, by randomized rounding, and within a Factor O(r2), if all requests have cardinality at most r. Expand SIGACT News Online Algorithms Column 36 • Computer Science • SIGACT News • 2020 This column will discuss some papers in online algorithms that appeared in 2020, and has instead made a selection. Expand #### References SHOWING 1-10 OF 51 REFERENCES Preemptive and non-preemptive generalized min sum set cover • Mathematics, Computer Science • Math. Program. • 2014 The linear programming relaxation and analysis are completely different from the aforementioned previous works and it is shown that any preemptive solution can be transformed into a non-preemptive one by losing a factor of 6.2 in the objective function. Expand Competitive Algorithms for Generalized k-Server in Uniform Metrics • Computer Science, Mathematics • SODA • 2018 The generalized k-server problem is considered in uniform metrics and the first f(k)-competitive algorithms for general k are given, including a deterministic and randomized algorithms with competitive ratio$O(k 2^k)$and$O (k^3 \log k)$respectively. Expand An Input Sensitive Online Algorithm for the Metric Bipartite Matching Problem • Mathematics, Computer Science • 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) • 2017 A novel input sensitive analysis of a deterministic online algorithm for the minimum metric bipartite matching problem and shows that the cost of edges of the optimal matching inside each larger ball can be shown to be proportional to the weight times the radius of the larger ball. Expand Approximating Min Sum Set Cover • Computer Science, Mathematics • Algorithmica • 2004 For the min sum vertex cover version of the problem, it is shown that it can be approximated within a ratio of 2, and is NP-hard to approximate within some constant ρ > 1. Expand A constant factor approximation algorithm for generalized min-sum set cover • Computer Science, Mathematics • SODA '10 • 2010 A simple randomized constant factor approximation algorithm is given for the generalized min-sum set cover problem, which is given a universe of elements and a collection of subsets with each set S having a covering requirement. Expand Chasing Convex Bodies Optimally The functional Steiner point of a convex function is defined and applied to the work function to obtain the algorithm achieving competitive ratio d for arbitrary normed spaces, which is exactly tight for$\ell^{\infty}$. Expand Stochastic Online Metric Matching • Computer Science, Mathematics • ICALP • 2019 The main result is an$O((\log \log n)^2)\$-competitive algorithm in this model, which implies a strict separation between the i.i.d model and the adversarial and random order models, both for general metrics and these much-studied metrics. Expand
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