Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Algorithms for Bandwidth and Storage Allocation Problems under Real Time Constraints
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Chordal Graphs and Their Clique Graphs
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
On the Complexity of Adjacent Resource Scheduling
Journal of Scheduling
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The clique-separator graph for chordal graphs
Discrete Applied Mathematics
The temporal knapsack problem and its solution
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
On the complexity of interval scheduling with a resource constraint
Theoretical Computer Science
Constant integrality gap LP formulations of unsplittable flow on a path
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Uncommon Dantzig-Wolfe Reformulation for the Temporal Knapsack Problem
INFORMS Journal on Computing
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We study a resource allocation problem where jobs have the following characteristic: each job consumes some quantity of a bounded resource during a certain time interval and induces a given profit. We aim to select a subset of jobs with maximal total profit such that the total resource consumed at any point in time remains bounded by the given resource capacity. While this case is trivially NP-hard in general and polynomially solvable for uniform resource consumptions, our main result shows the NP-hardness for the case of general resource consumptions but uniform profit values, i.e. for the case of maximizing the number of performed jobs. This result applies even for proper time intervals. We also give a deterministic (1/2-@e)-approximation algorithm for the general problem on proper intervals improving upon the currently known 1/3 ratio for general intervals. Finally, we study the worst-case performance ratio of a simple greedy algorithm.