We investigate the problem of computing a minimum volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NPhard so that we cannot expect to find exact polynomial time algorithms. We give constant ratio approximation algorithms for packing axis-parallel (rectangular) cuboids under translation into an a...

We describe sequential and parallel algorithms that approximately solve linear programs with no negative coefficients (a.k.a. mixed packing and covering problems). For explicitly given problems, our fastest sequential algorithm returns a solution satisfying all constraints within a 1 ± ǫ factor in O(md log(m)/ǫ) time, where m is the number of constraints and d is the maximum number of constrain...

Packing and covering linear programs belong to the narrow class of linear programs that are efficiently solvable in parallel and distributed models of computation, yet are a powerful modeling tool for a wide range of fundamental problems in theoretical computer science, operations research, and many other areas. Following recent progress in obtaining faster distributed and parallel algorithms f...

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number of accepted items or accepted volume. This paper presents results for the opposite problems, where we want to maximize the number of bins used or minimize the number of accepted items or the accepted volume. For the off-line variant, we require that t...

Good algorithms exist for solving the 2D rectangular strip packing problem when the objective is to minimize the amount of wasted material. However, in some applications other criteria are also important. We describe new heuristics for strip packing that optimize not only for wastage, but also for the efficient use of the cutting equipment, by minimizing the number of independent cuts required ...

We have developed a novel approach to solve the protein side-chain packing problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique. Since our approach is based on deterministic algorithms in contrast to the various existing algorithms base...

This article presents a simple algorithm for packing sparse 2-D arrays into minimal I-D arrays in O(r?) time. Retrieving an element from the packed I-D array is O(l). This packing algorithm is then applied to create minimal perfect hashing functions for large word lists. Many existing perfect hashing algorithms process large word lists by segmenting them into several smaller lists. The perfect ...

We study an on-line bin packing problem. A xed number n of bins, possibly of diierent sizes, are given. The items arrive on-line, and the goal is to pack as many items as possible. It is known that there exists a legal packing of the whole sequence in the n bins. We consider fair algorithms that reject an item, only if it does not t in the empty space of any bin. We show that the competitive ra...

We obtain a necessary and su cient condition for tournaments to possess a min-max relation on packing and covering directed cycles, together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem in this class of tournaments; the condition and the algorithms are all based on a totally dual integral system, a theoretical framework introduced by...

Cutting and packing problems are encountered in many industries, with different industries incorporating different constraints and objectives. The wood-, glassand paper industry are mainly concerned with the cutting of regular figures, whereas in the ship building, textile and leather industry irregular, arbitrary shaped items are to be packed. In this paper two genetic algorithms are described...