Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Approximability of scheduling with fixed jobs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
Approximate Max-Min Resource Sharing for Structured Concave Optimization
SIAM Journal on Optimization
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Approximation algorithms for scheduling with reservations
HiPC'07 Proceedings of the 14th international conference on High performance computing
Parameterized Complexity and Approximation Algorithms
The Computer Journal
Improved approximation algorithms for scheduling with fixed jobs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Survey on Approximation Algorithms for Scheduling with Machine Unavailability
Algorithmics of Large and Complex Networks
There is no EPTAS for two-dimensional knapsack
Information Processing Letters
Theoretical Computer Science
| Hi-index | 0.00 |
The multiple knapsack problem (MKP) is a well-known generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins (knapsacks) such that each item a ∈ A has a size size(a) and a profit value profit(a), and each bin b ∈ B has a capacity c(b). The goal is to find a subset U ⊂ A of maximum total profit such that U can be packed into B without exceeding the capacities. The decision version of MKP is strongly NP-complete, since it is a generalization of the classical knapsack and bin packing problem. Furthermore, MKP does not admit an FPTAS even if the number m of bins is two. Kellerer gave a PTAS for MKP with identical capacities and Chekuri and Khanna presented a PTAS for MKP with general capacities with running time nO(log(1/ε)/ε8). In this paper we propose an EPTAS with parameterized running time 2O(log(1/ε)/ε5) · poly(n) + O(m) for MKP. This solves also an open question by Chekuri and Khanna.