A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
Staff scheduling for inbound call centers and customer contact centers
IAAI'02 Proceedings of the 14th conference on Innovative applications of artificial intelligence - Volume 1
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Resource allocation for covering time varying demands
ESA'11 Proceedings of the 19th European conference on Algorithms
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Consider the following problem which often arises in contact center scheduling scenarios. We are given a set of employees where each employee can be deployed for shifts consisting of L consecutive time units. Further, each employee specifies a set of possible start times, and can be deployed for a bounded number of shifts only. At each point of time t, we are also given a lower bound rt on the number of employees that should be present at this time. The goal is to find a schedule for the employees such that the number of time slots whose requirements are met is maximized. Such problems naturally arise in many other situations, e.g., sensor networks and cloud computing. The strict nature of the resource requirement makes this problem very hard to approximate. In this paper, we give a bicriteria approximation algorithm for this problem. Given a parameter ε 0, we give an O(1/ε3 log 1ε)-approximation algorithm for this problem, where we count those time slots for which we satisfy at least (1-ε)-fraction of the requirement. Our techniques involve a configuration LP relaxation for this problem, and we use non-trivial structural properties of an optimal solution to solve this LP relaxation. We even consider the more general problem where shift lengths of different employees can vary significantly. In this case, we show that even finding a good bicriteria approximation is hard (under standard complexity theoretic assumptions).