Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
On the minimization of the makespan subject to flowtime optimality
Operations Research
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A generalized bound on LPT sequencing
SIGMETRICS '76 Proceedings of the 1976 ACM SIGMETRICS conference on Computer performance modeling measurement and evaluation
Scheduling chain-structured tasks to minimize makespan and mean flow time
Information and Computation
NP-complete scheduling problems
Journal of Computer and System Sciences
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In job scheduling with precedence constraints, i ≺ j means that job j cannot start being processed before job i is completed. In this paper we consider selfish bully jobs who do not let other jobs start their processing if they are around. Formally, we define the selfish precedence-constraint where i ≺s j means that j cannot start being processed if i has not started its processing yet. Interestingly, as was detected by a devoted kindergarten teacher whose story is told below, this type of precedence constraints is very different from the traditional one, in a sense that problems that are known to be solvable efficiently become NP-hard and vice-versa. The work of our hero teacher, Ms. Schedule, was initiated due to an arrival of bully jobs to her kindergarten. Bully jobs bypass all other nice jobs, but respect each other. This natural environment corresponds to the case where the selfish precedence-constraints graph is a complete bipartite graph. Ms. Schedule analyzed the minimum makespan and the minimum total flow-time problems for this setting. She then extended her interest to other topologies of the precedence constraints graph and other special instances with uniform length jobs and/or release times.