A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
The Multiple Subset Sum Problem
SIAM Journal on Optimization
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Parameterized Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Parameterized Complexity and Approximation Algorithms
The Computer Journal
Tight approximation algorithms for scheduling with fixed jobs and nonavailability
ACM Transactions on Algorithms (TALG)
Approximation algorithms for scheduling and packing problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Scheduling jobs on identical and uniform processors revisited
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Bounding the running time of algorithms for scheduling and packing problems
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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In this paper we propose an improved efficient approximation scheme for the multiple knapsack problem (MKP). Given a set ${\mathcal A}$ of n items and set ${\mathcal B}$ of m bins with possibly different capacities, the goal is to find a subset $S \subseteq{\mathcal A}$ of maximum total profit that can be packed into ${\mathcal B}$ without exceeding the capacities of the bins. Chekuri and Khanna presented a PTAS for MKP with arbitrary capacities with running time $n^{O(1/\epsilon^8 \log(1/\epsilon))}$ . Recently we found an efficient polynomial time approximation scheme (EPTAS) for MKP with running time $2^{O(1/\epsilon^5 \log(1/\epsilon))} poly(n)$ . Here we present an improved EPTAS with running time $2^{O(1/\epsilon \log^4(1/\epsilon))} + poly(n)$ . If the integrality gap between the ILP and LP objective values for bin packing with different sizes is bounded by a constant, the running time can be further improved to $2^{O(1/\epsilon \log^2(1/\epsilon))} + poly(n)$ .