We propose two new heuristics to pack unequal circles into a two dimensional circular container. The first one, denoted by A1.0, is a basic heurisitc which selects the next circle to place according to the maximal hole degree rule. The second one, denoted by A1.5, uses a self lookahead strategy to improve A1.0. We evaluate A1.0 and A1.5 on a series of instances up to 100 circles from the litera...

We consider two well-known natural variants of bin packing, and show that these packing problemsadmit asymptotic fully polynomial time approximation schemes (AFPTAS). In bin packing problems,a set of one-dimensional items of size at most 1 is to be assigned (packed) to subsets of sum at most1 (bins). It has been known for a while that the most basic problem admits an AFPTAS. In this...

In this paper, we consider the online three-dimensional container loading problem. We develop a novel online packing algorithm to solve the threedimensional bin packing problem in the online case where items are not know well in advance and they have to be packed in real-time when they arrive. This is relevant in many real-world scenarios such as automated cargo loading in warehouses. This is a...

The edge and vertex-disjoint path problems together with their unsplittable flow generalization are NP-hard problems with a multitude of applications in areas such as routing, scheduling and bin packing. Given the hardness of the problems, we study polynomial-time approximation algorithms with bounded performance guarantees. We introduce techniques which yield new algorithms for a wide range of...

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...

Packing problems deal with loading of a set of items (objects) into a set of boxes (containers) in order to optimize a performance criterion under various constraints. With the advance of RFID technologies and investments in IT infrastructures companies now have access to the necessary data that can be utilized in cost reduction of packing processes. Therefore bin packing and container loading ...

In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We consider a version of the problem where there is no ordering among the items. We present exact, linear-time algorithms for this problem for the cases where there are two or more color...

The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of re...