On Lazy Bin Covering and Packing problems

AbstractIn this paper, we study two interesting variants of the classical bin packing problem, called Lazy Bin Covering (LBC) and Cardinality Constrained Maximum Resource Bin Packing (CCMRBP) problems. For the offline LBC problem, we first prove the approximation ratio of the First-Fit-Decreasing and First-Fit-Increasing algorithms, then present an APTAS. For the online LBC problem, we give a competitive analysis for the algorithms of Next-Fit, Worst-Fit, First-Fit, and a modified HARMONICM algorithm. The CCMRBP problem is a generalization of the Maximum Resource Bin Packing (MRBP) problem Boyar et al. (2006) [1]. For this problem, we prove that its offline version is no harder to approximate than the offline MRBP problem

Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

Randomized Parameterized Algorithms for the Kidney Exchange Problem

In order to increase the potential kidney transplants between patients and their incompatible donors, kidney exchange programs have been created in many countries. In the programs, designing algorithms for the kidney exchange problem plays a critical role. The graph theory model of the kidney exchange problem is to find a maximum weight packing of vertex-disjoint cycles and chains for a given weighted digraph. In general, the length of cycles is not more than a given constant L (typically 2 L 5), and the objective function corresponds to maximizing the number of possible kidney transplants. In this paper, we study the parameterized complexity and randomized algorithms for the kidney exchange problem without chains from theory. We construct two different parameterized models of the kidney exchange problem for two cases L = 3 and L 3, and propose two randomized parameterized algorithms based on the random partitioning technique and the randomized algebraic technique, respectively

Modelling of amorphous polymer surfaces in computer simulation

We study surface effects in amorphous polymer systems by means of computer simulation. In the framework of molecular dynamics, we present two different methods to prepare such surfaces. {\em Free} surfaces are stabilized solely by van--der--Waals interactions whereas {\em confined} surfaces emerge in the presence of repelling plates. The two models are compared in various computer simulations. For free surfaces, we analyze the migration of end--monomers to the surface. The buildup of density and pressure profiles from zero to their bulk values depends on the surface preparation method. In the case of confined surfaces, we find density and pressure oszillations next to the repelling plates. We investigate the influence of surfaces on the coordination number, on the orientation of single bonds, and on polymer end--to--end vectors. Furthermore, different statistical methods to determine location and width of the surface region for systems of various chain lengths are discussed and applied. We introduce a ``height function'' and show that this method allows to determine average surface profiles only by scanning the outermost layer of monomers.Comment: 23 pages, 12 figure