On the complexity of privacy-preserving complex event processing
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Submodular function minimization under a submodular set covering constraint
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Nonmonotone submodular maximization via a structural continuous greedy algorithm
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Submodular cost allocation problem and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Generalized roof duality and bisubmodular functions
Discrete Applied Mathematics
Ranking with submodular valuations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Evader interdiction and collateral damage
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
SIAM Journal on Computing
LP-Based covering games with low price of anarchy
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
| Hi-index | 0.00 |
This paper addresses the problems of minimizing nonnegative submodular functions under covering constraints, which generalize the vertex cover, edge cover, and set cover problems. We give approximation algorithms for these problems exploiting the discrete convexity of submodular functions. We first present a rounding 2-approximation algorithm for the submodular vertex cover problem based on the half-integrality of the continuous relaxation problem, and show that the rounding algorithm can be performed by one application of submodular function minimization on a ring family. We also show that a rounding algorithm and a primal-dual algorithm for the submodular cost set cover problem are both constant factor approximation algorithms if the maximum frequency is fixed. In addition, we give an essentially tight lower bound on the approximability of the submodular edge cover problem.