Inverse Bin-Packing Number Problems: Polynomially Solvable Cases
نویسنده
چکیده
Consider the inverse bin-packing number problem. Given a set of items and a prescribed number K of bins, the inverse bin-packing number problem, IBPN for short, is concerned with determining the minimum perturbation to the itemsize vector so that all the items can be packed into K bins or less. It is known that this problem is NP-hard (Chung, 2012 ). In this paper, we investigate some special cases of IBPN that can be solved in polynomial time. We propose an optimal algorithm for solving the IBPN instances with two distinct item sizes and the instances with large items.
منابع مشابه
Bin Packing with Fixed Number of Bins Revisited
As Bin Packing is NP-hard already for k = 2 bins, it is unlikely to be solvable in polynomial time even if the number of bins is a fixed constant. However, if the sizes of the items are polynomially bounded integers, then the problem can be solved in time n for an input of length n by dynamic programming. We show, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in u...
متن کاملThe column-circular, subsets-selection problem: complexity and solutions
In this paper we study the complexity of a new class of a problem that we call the column-circular, subsets-selection problem and we show that, under a special condition, it is a polynomially solvable problem. First, we show that the column-circular set-partitioning, the column-circular set-covering, and the columncircular set-packing problems, among others, are special cases of the problem con...
متن کاملSingle-machine scheduling against due dates with past-sequence-dependent setup times
Recently Koulamas and Kyparisis (2006) introduced past-sequence-dependent setup times to scheduling problems. This means that the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. Koulamas and Kyparisis (2006) were able to show for a number of single-machine scheduling problems with completion time goals that they remain polynomially solvable. In...
متن کاملChapter 18 APPROXIMATION ALGORITHMS
Most interesting real-world optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a near-optimal solution to a large-scale optimization problem may require computational resources far beyond what is practically available. There is a substantial body of literature exploring the computational properties of optimization prob...
متن کاملSolving the Multi-Resource Bin Packing Problem with a Reordering Grouping Genetic Algorithm
We formally define multi-resource bin packing, a generalization of conventional bin packing, and develop an algorithm called Reordering Grouping Genetic Algorithm (RGGA) to solve this problem. Multi-resource bin packing can be applied to different problems, such as placing virtual machines onto servers. We first test RGGA on conventional bin packing problems and show that it yields excellent re...
متن کامل