It is shown that for any positive E the strip-packing problem, i.e. the problem of packing a given list of rectangles into a strip of width 1 and minimum height. can be solled within I c 2: times the optimal height, in linear time, if the heights and widths of these rectangles are all bounded below by an absolute constant 2 >O. @ 1998 Elsevicr Science B.V. All rights reserved. K~YIYJY~/S: Strip...

In the d-dimensional online bin packing problem, cubes of positive sizes no larger than 1 are presented one by to be assigned positions in unit cube bins. this work, we provide improved upper bounds on asymptotic competitive ratio for square and problems, where our do not exceed 2.0885 2.5735 packing, respectively. To achieve these results, adapt improve a previously designed harmonic-type algo...

In many problems, the inputs to the problem arrive over time. As each input is received, it must be dealt with irrevocably. Such problems are online problems. An increasingly common method of solving online problems is to solve the corresponding linear program, obtained either directly for the problem or by relaxing the integrality constraints. If required, the fractional solution obtained is t...

The Problem: A number of powerful optimization techniques have been developed to deal with different aspects of molecular design problems that arise in biology and biological engineering, including the design of protein folds and protein binding interfaces. The two key examples are algorithms for optimizing packing interactions and a separate approach for optimizing electrostatic interactions. ...

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size si ∈ [0, 1] and a color ci ∈ C, where C is a set of colors (that is not necessarily known in advance). The total size of items packed into a bin cannot exceed its size, thus an item i can always be packed into a ...

The bin packing optimization problem packs a set of objects into a set of bins so that the amount of wasted space is minimized The bin packing problem has many important applications These include multiprocessor scheduling resource allocation and real world planning packing routing and scheduling optimization problems The bin packing problem is NP complete Since there is therefore little hope i...

We analyze approximation algorithms for bounded-space bin packing by comparing them against the optimal bounded-space packing (instead of comparing them against the globally optimal packing that does not necessarily satisfy the bounded-space constraint). For 2-boundedspace bin packing we construct a polynomial time offline approximation algorithm with asymptotic worst case ratio 3/2, and we sho...