An optimal algorithm for on-line bipartite matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Online computation and competitive analysis
Online computation and competitive analysis
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Performance Guarantees for Hierarchical Clustering
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
Approximation algorithms for hierarchical location problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Adaptivity and approximation for stochastic packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Some results on incremental vertex cover problem
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Dense subgraph maintenance under streaming edge weight updates for real-time story identification
Proceedings of the VLDB Endowment
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Many combinatorial optimization problems aim to select a subset of elements of maximum value subject to certain constraints. We consider an incremental version of such problems, in which some of the constraints rise over time. A solution is a sequence of feasible solutions, one for each time step, such that later solutions build on earlier solutions incrementally. We introduce a general model for such problems, and define incremental versions of maximum flow, bipartite matching, and knapsack. We find that imposing an incremental structure on a problem can drastically change its complexity. With this in mind, we give general yet simple techniques to adapt algorithms for optimization problems to their respective incremental versions, and discuss tightness of these adaptations with respect to the three aforementioned problems.