In this paper, we present a novel O(N) algorithm to minimize the weighted number of tardy jobs with unit processing times, integer ready times and deadlines, and M homogeneous parallel machines, where N is the number of jobs to be scheduled. wi is the weight re ecting job i's importance, and Ui is 1 if job i is tardy and 0 otherwise, so P wiUi is the measure of performance. (In standard notatio...

We consider directed graphs with edge labels from a semiring. We present an algorithm that allows efficient execution of queries for existence and weights of paths, and allows updates of the graph: adding nodes and edges, and changing weights of existing edges. We apply this method in the construction of matchbound certificates for automatically proving termination of string rewriting. We re-im...

This paper is about scheduling parallel jobs, i.e. which can be executed on more than one machine at the same time. Malleable jobs is a special class of parallel jobs. The number of machines a malleable job is executed on may change during its execution. In this work, we consider the NP-hard problem of scheduling malleable jobs to minimize the total weighted completion time (or mean weighted fl...

4. Weighted sum of completion times 1 Eugene L. Lawler, Maurice Queyranne, Andreas S. Schulz, David B. Shmoys 4.1. Smith’s ratio rule 2 4.2. Preference orders on jobs 5 4.3. Preference orders on sequences and series-parallel precedence constraints 8 4.4. NP-hardness of further constrained min-sum problems 14 4.5. The ratio rule via linear programming 18 4.6. Approximation algorithms for 1|prec|...

Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is tensor analog that attempts to impute from similar low-rank type assumptions. In this paper, we study when sampling pattern deterministic possibly non-uniform. We first propose an efficient weighted High...

We consider the problem of minimizing the weighted sum of job completion times on a single machine (subject to certain job weights) with an additional side constraint on the weighted sum of job completion times (with respect to different job weights). This problem is NP-hard, and we provide a polynomial time approximation scheme for this problem. Our method is based on Lagrangian relaxation mix...

We study the problem of minimizing the average weighted completion time on a single machine under the additional constraint that the sum of completion times does not exceed a given bound B (1 !Cj B !wjCj) for which we propose a 2 1 -approximationalgorithm. We also address the problem1 !c jCj B !wjCj for which we present a 2 2 -approximation algorithm. After showing that the problem of minimizin...

In this paper we consider a single machine scheduling problem with deteriorating jobs. By deteriorating jobs, we mean that the processing time of a job is a simple linear function of its execution starting time. For the jobs with chain precedence constraints, we prove that the weighted sum of squared completion times minimization problem with strong chains and weak chains can be solved in polyn...

Flow shop problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider a bi-criteria permutation flow shop scheduling problem, where weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in strong sense, an effective multi-objectiv...