An 0.828–approximation algorithm for the uncapacitated facility location problem
Discrete Applied Mathematics
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Journal of the ACM (JACM)
On the submodularity of influence in social networks
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Cost-effective outbreak detection in networks
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Maximizing Non-Monotone Submodular Functions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A combinatorial allocation mechanism with penalties for banner advertising
Proceedings of the 17th international conference on World Wide Web
Optimal auctions with positive network externalities
Proceedings of the 12th ACM conference on Electronic commerce
Mechanism design with uncertain inputs: (to err is human, to forgive divine)
Proceedings of the forty-third annual ACM symposium on Theory of computing
Recoverable values for independent sets
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Optimal Auctions with Positive Network Externalities
ACM Transactions on Economics and Computation - Special Issue on Algorithmic Game Theory
| Hi-index | 0.00 |
We introduce a new framework for designing and analyzing algorithms. Our framework applies best to problems that are inapproximable according to the standard worst-case analysis. We circumvent such negative results by designing guarantees for classes of instances, parameterized according to properties of the optimal solution. We also make sure that our parameterized approximation, called PArametrized by the Signature of the Solution (PASS) approximation, is the best possible. We show how to apply our framework to problems with additive and submodular objective functions such as the capacitated maximum facility location problems. We consider two types of algorithms for these problems. For greedy algorithms, our framework provides a justification for preferring a certain natural greedy rule over some alternative greedy rules that have been used in similar contexts. For LP-based algorithms, we show that the natural LP relaxation for these problems is not optimal in our framework. We design a new LP relaxation and show that this LP relaxation coupled with a new randomized rounding technique is optimal in our framework. In passing, we note that our results strictly improve over previous results of Kleinberg, Papadimitriou and Raghavan [JACM 2004] concerning the approximation ratio of the greedy algorithm.