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...

We solve the problem of decomposing a rectangle R into p rectangles of equal area so that the maximum rectangle perimeter is as small as possible. This work has applications in areas such as flexible object packing and data allocation. Our solution requires only a constant number of arithmetic operations and integer square roots to characterize the decomposition, and linear time to print the de...

the search for new stationary phases has been one of the predominant concerns in high performance liquid chromatography (hplc) in order to achieve better resolutions, longer column lives, and reduce the time of analysis. a chromatographic packing for separation of underivatized amino acids (aas) were prepared by dynamically coating 2-amino tetraphenyl prophyrin (atpp) on a c-18 reversed-phase p...

Abstract. The bin packing problem is to pack a list of reals in (0, 1] into unit-capacity bins using the minimum number of bins. Let R[A] be the limiting worst value for the ratio A(L)/L* as L* goes to x, where A(L) denotes the number ofbins used in the approximation algorithm A, and L* denotes the minimum number ofbins needed to pack L. Obviously, R[A] reflects the worst-case behavior of A. Fo...

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 c...

We show that a modification of the Kenyon-Remila algorithm for the strip-packing problem yields an improved bound on the value of the approximate solution. As a corollary we derive that there exists a polynomial-time algorithm that always finds a solution of value OPT +O( √ OPT logOPT ) where OPT is the optimal value.

This work is based on Mohar [1]’s recent algorithm for circle packing for the Euclean case. We implement his polynomial time algorithm for constructing primal-dual circle packings of almost 3-connected planar maps. We have improved Mohar’s algorithm and have been able to get near an order of magnitude speed up for large graphs. We describe our implementation in C/C++ style pseudo-code.