conclusions the mssrhs could be considered as a more suitable packing material for long-term biofilter operation to remove h2s pollution. results in this study, after 53 days of operating time and 54 g/m3h mass loading, the ph values in the ss and mssrhs packed filters were reduced from 6.8 to 1.8 and from 6.9 to 3.4, respectively. the mssrhs packed filter showed more buffering capacity to resi...

The 2-dimensional Bin Packing problem is a generalization of the classical Bin Packing problems and is defined as follows: Given a collection of rectangles specified by their width and height, the goal is to pack these into minimum number of square bins of unit size. Recently, the problem was proved to be APX-hard even in the asymptotic case, i.e. when the optimum solutions requires a large num...

In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. [7] in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust algorithms for online problems. We apply our ne...

The multiple knapsack problem (MKP) is a well-known generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins (knapsacks) such that each item a ∈ A has a size size(a) and a profit value profit(a), and each bin b ∈ B has a capacity c(b). The goal is to find a subset U ⊂ A of maximum total profit such that U can be packed into B without exceeding the ca...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical N P-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a ...

The d-dimensional vector packing problem is a well-known generalization of the classical bin packing problem: For a given list of vectors in [ 0, 1 ] d, the goal is to partition the list into the minimum number of subsets, such that in every subset the sum of all vectors is at most one in every coordinate. For the case d = 1, Femandez de la Vega and Lueker ( 1981) designed an asymptotic polynom...

“Bin packing with rejection” is the following problem: Given a list of items with associated sizes and rejection costs, find a packing into unit bins of a subset of the list such that the number of bins used plus the sum of rejection costs of unpacked items is minimized. We show that bin packing with rejection can be reduced to n multiple knapsack problems and, based on techniques for the multi...

In the bin covering problem there is a group L=(a1; : : : ; an) of items with sizes s̃(ai)∈ (0; 1), and the goal is to 6nd a packing of the items into bins to maximize the number of bins that receive items of total size at least 1. This is a dual problem to the classical bin packing problem. In this paper we present the 6rst asymptotic fully polynomial-time approximation scheme for the problem. ...

Let S be any family of n c-oriented polygons of the two-dimensional Euclidean plane E, i.e., bounded intersection of halfplanes whose normal directions of edges belong to a .xed collection of c distinct directions. Let (S) denote the packing number of S, that is the maximum number of pairwise disjoint objects of S. Let (S) be the transversal number of S, that is the minimum number of points req...