Best packing of rods into boxes
Discrete Mathematics
An Algorithm for Scheduling Jobs in Hypercube Systems
IEEE Transactions on Parallel and Distributed Systems
On multi-dimensional packing problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Complexity theory on real numbers and functions
Proceedings of the 6th GI-Conference on Theoretical Computer Science
A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing
Mathematics of Operations Research
A Tale of Two Dimensional Bin Packing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved approximation algorithms for multidimensional bin packing problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
An Exact Algorithm for Higher-Dimensional Orthogonal Packing
Operations Research
A Maximal-Space Algorithm for the Container Loading Problem
INFORMS Journal on Computing
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
Hardness of Approximating Flow and Job Shop Scheduling Problems
Journal of the ACM (JACM)
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This paper proposes a four dimensional orthogonal packing and time scheduling problem. The problem differs from the classical packing problems in that the position and orientation of each item in the container can be changed over time. In this way, the four dimensional space-time problem better uses the container time. Also, we consider a general case that all parameters are real numbers, which makes the problems more difficult to solve. This paper proposes an algorithm and proves that the algorithm could solve the problem optimally by a finite number of operations. We say this problem is weak computational, meaning that if there exists a universal machine that could represent real numbers and could do unit arithmetic or logical operation on real numbers in finite time, then the algorithm could find optimal solutions in finite time. This paper also presents a proof of the weak computability over a general case of the three dimensional orthogonal packing problem where all parameters are positive real numbers.