A fast algorithm for multiprocessor scheduling of unit-length jobs
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A faster strongly polynomial minimum cost flow algorithm
Operations Research
ACM Transactions on Computer Systems (TOCS)
Minimizing stall time in single and parallel disk systems
Journal of the ACM (JACM)
Handbook of Theoretical Computer Science: Algorithms and Complexity
Handbook of Theoretical Computer Science: Algorithms and Complexity
A fast algorithm for single processor scheduling
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Integrated prefetching and caching in single and parallel disk systems
Information and Computation
Online scheduling of parallel jobs on hypercubes: maximizing the throughput
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Parallel machine problems with equal processing times: a survey
Journal of Scheduling
Open problems in throughput scheduling
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally unimodular. Still, sometimes it is possible to build an integer solution with same cost from the fractional solution. Examples are two scheduling problems [4,5] and the single disk prefetching/caching problem [3]. We show that problems such as the three previously mentioned can be separated into two subproblems: (1) finding an optimal feasible set of slots, and (2) assigning the jobs or pages to the slots. It is straigthforward to show that the latter can be solved greedily. We are able to solve the former with a totally unimodular linear program, from which we obtain simple combinatorial algorithms with improved worst case running time.