Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
On chromatic sums and distributed resource allocation
Information and Computation
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
A sharp concentration inequality with application
Random Structures & Algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Min-sum Set Cover
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating Min Sum Set Cover
Algorithmica
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
An approximation algorithm for the minimum latency set cover problem
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The pipelined set cover problem
ICDT'05 Proceedings of the 10th international conference on Database Theory
Approximation algorithms for diversified search ranking
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
A primal-dual approximation algorithm for min-sum single-machine scheduling problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Ranking with submodular valuations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Minimum latency submodular cover
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Consider the following generalized min-sum set cover or multiple intents re-ranking problem proposed by Azar et al. (STOC 2009). We are given a universe of elements and a collection of subsets, with each set S having a covering requirement of K(S). The objective is to pick one element at a time such that the average covering time of the sets is minimized, where the covering time of a set S is the first time at which K(S) elements from it have been selected. There are two well-studied extreme cases of this problem: (i) when K(S) = 1 for all sets, we get the min-sum set cover problem, and (ii) when K(S) = |S| for all sets, we get the minimum-latency set cover problem. Constant factor approximations are known for both these problems. In their paper, Azar et al. considered the general problem and gave a logarithmic approximation algorithm for it. In this paper, we improve their result and give a simple randomized constant factor approximation algorithm for the generalized min-sum set cover problem.