Three partition refinement algorithms
SIAM Journal on Computing
Computing a perfect edge without vertex elimination ordering of a chordal bipartite graph
Information Processing Letters
Treewidth of chordal bipartite graphs
Journal of Algorithms
Approximation algorithms for NP-hard problems
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Graph classes: a survey
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Greedily finding a dense subgraph
Journal of Algorithms
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
Two-Dimensional Gantt Charts and a Scheduling Algorithm of Lawler
SIAM Journal on Discrete Mathematics
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Partially-Ordered Knapsack and Applications to Scheduling
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Discrete Applied Mathematics
A strengthened formulation and cutting planes for the open pit mine production scheduling problem
Computers and Operations Research
Approximation algorithms for the sex-equal stable marriage problem
ACM Transactions on Algorithms (TALG)
Sharing-aware algorithms for virtual machine colocation
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
The 1-neighbour knapsack problem
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
The knapsack problem with neighbour constraints
Journal of Discrete Algorithms
LAD models, trees, and an analog of the fundamental theorem of arithmetic
Discrete Applied Mathematics
Approximations for the Two-Machine Cross-Docking Flow Shop Problem
Discrete Applied Mathematics
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In the partially ordered knapsack problem (POK) we are given a set N of items and a partial order @?"P on N. Each item has a size and an associated weight. The objective is to pack a set N^'@?N of maximum weight in a knapsack of bounded size. N^' should be precedence-closed, i.e., be a valid prefix of @?"P. POK is a natural generalization, for which very little is known, of the classical Knapsack problem. In this paper we present both positive and negative results. We give an FPTAS for the important case of a two-dimensional partial order, a class of partial orders which is a substantial generalization of the series-parallel class, and we identify the first non-trivial special case for which a polynomial-time algorithm exists. Our results have implications for approximation algorithms for scheduling precedence-constrained jobs on a single machine to minimize the sum of weighted completion times, a problem closely related to POK.