Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On chromatic sums and distributed resource allocation
Information and Computation
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Approximating Min Sum Set Cover
Algorithmica
Personalizing search via automated analysis of interests and activities
Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval
Improving web search ranking by incorporating user behavior information
SIGIR '06 Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval
Evaluating the accuracy of implicit feedback from clicks and query reformulations in Web search
ACM Transactions on Information Systems (TOIS)
A large-scale evaluation and analysis of personalized search strategies
Proceedings of the 16th international conference on World Wide Web
Submodular function minimization
Mathematical Programming: Series A and B
Faster and Simpler Algorithms for Multicommodity Flow and Other Fractional Packing Problems
SIAM Journal on Computing
A user browsing model to predict search engine click data from past observations.
Proceedings of the 31st annual international ACM SIGIR conference on Research and development in information retrieval
Novelty and diversity in information retrieval evaluation
Proceedings of the 31st annual international ACM SIGIR conference on Research and development in information retrieval
A Faster Strongly Polynomial Time Algorithm for Submodular Function Minimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Approximating submodular functions everywhere
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A simple combinatorial algorithm for submodular function minimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the Second ACM International Conference on Web Search and Data Mining
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
Submodular Function Minimization under Covering Constraints
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximability of Combinatorial Problems with Multi-agent Submodular Cost Functions
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Optimal Long Code Test with One Free Bit
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A constant factor approximation algorithm for generalized min-sum set cover
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
$O(\sqrt{\logn})$ Approximation to SPARSEST CUT in $\tilde{O}(n^2)$ Time
SIAM Journal on Computing
An approximation algorithm for the minimum latency set cover problem
ESA'05 Proceedings of the 13th annual European conference on 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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We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set [m], and a collection of n monotone sub-modular set functions f1,...,fn, where each function fi: 2[m] → R+. An additional input ingredient is a weight vector w ∈ Rn+. The goal is to find a linear ordering of the ground set elements that minimizes the weighted cover time of the functions. The cover time of a function is the minimal number of elements in the prefix of the linear ordering that form a set whose corresponding function value is greater than a unit threshold value. Our main result is an O(ln(1/∈))-approximation algorithm for the problem, where ε is the smallest nonzero marginal value that any function may gain from some element. Our algorithm orders the elements using an adaptive residual updates scheme, which may be of independent interest. We also prove that the problem is Ω(ln(1/∈))-hard to approximate, unless P = NP. This implies that the outcome of our algorithm is optimal up to constant factors.