Polygon scheduling

Consider a set of circles of the same length and r irregular polygons with vertices on a circle of this length. Each of the polygons has to be arranged on a given subset of all circles and the positions of the polygon on the different circles are depending on each other. How should the polygons be arranged relative to each other to minimize some criterion function depending on the distances between adjacent vertices on all circles? A decomposition of the set of all arrangements of the polygons into local regions in which the optimization problem is convex is given. An exact description of the local regions and a sharp bound on the number of local regions are derived. For the criterion functions minimizing the maximum weighted distance, maximizing the minimum weighted distance, and minimizing the sum of weighted distances the local optimization problems can be reduced to polynomially solvable network flow problems

Quality of Move-Optimal Schedules for Minimizing the Vector Norm of the Workloads

We study the problem of minimizing the vector norm $||\cdot||_p$ of the workloads. We examine move-optimal assignments and prove a performance guarantee of $\frac{2^p-1}{p} \cdot \left(\frac{p-1}{2^p-2}\right)^{\frac{p-1}{p}},$ for any integer $p>1$ and moreover, we show that this guarantee is tight. Additionally, we consider assignments obtained by applying the LPT-heuristic of Graham (1969). We prove that an LPT-assignment has a performance guarantee of $\frac{3^p-2^p}{p} \cdot \left(\frac{p-1}{2 \cdot 3^p - 3 \cdot 2^p}\right)^{\frac{p-1}{p}},$ which reproves a result of Chandra and Wong (1975)

Approximating Minimum Independent Dominating Sets in Wireless Networks

We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a (1+")- pproximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network

Two exponential neighborhoods for single machine scheduling

We study the problem of minimizing total completion time on a single machine with the presence of release dates. We present two different approaches leading to exponential neighborhoods in which the best improving neighbor can be determined in polynomial time. Furthermore, computational results are presented to get insight in the performance of the developed neighborhoods

A tabu search algorithm for scheduling a single robot in a job-shop environment

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the travelling-salesman problem with time windows, where additionally generalized precedence constraints have to be respected. The objective is to determine a sequence of all nodes and corresponding starting times in the given time windows in such a way that all generalized precedence relations are respected and the sum of all travelling and waiting times is minimized. We present a local search algorithm for this problem where an appropriate neighborhood structure is defined using problem-specific properties. In order to make the search process more efficient, we apply some techniques which accelerate the evaluation of the solutions in the proposed neighbourhood considerably. Computational results are presented for test data arising from job-shop instances with a single transport robot

Tabu search algorithms for job-shop problems with a single transport robot

We consider a generalized job-shop problem where the jobs additionally have to be transported between the machines by a single transport robot. Besides transportation times for the jobs, empty moving times for the robot are taken into account. The objective is to determine a schedule with minimal makespan. \u

Online Bivariate Outlier Detection in Final Test Using Kernel Density Estimation

In parametric IC testing, outlier detection is applied to filter out potential unreliable devices. Most outlier detection methods are used in an offline setting and hence are not applicable to Final Test, where immediate pass/fail decisions are required. Therefore, we developed a new bivariate online outlier detection method that is applicable to Final Test without making assumptions about a specific form of relations between two test parameters. An acceptance region is constructed using kernel density estimation. We use a grid discretization in order to enable a fast outlier decision. After each accepted device the grid is updated, hence the method is able to adapt to shifting measurements

Resource Management in Heterogeneous Wireless Sensor Networks

We propose a first approach in the direction of a general framework for resource management in wireless sensor networks (WSN). The basic components of the approach are a model for WSNs and a task model. Based on these models, a first version of an algorithm for assigning tasks to a WSN is presented. The models and the algorithm are designed in such a way that an extension to more complex models is possible. Furthermore, the developed approach to solve the RM problem allows an easy adaptation, to fit more complex models. In this way, a flexible approach is achieved, which may form the base for many RM approaches.\ud The possibilities and limitations of the presented approach are tested on randomly generated instances. The aim of these tests is to show that the chosen models and algorithm form a proper starting point to design RM tools

Cyclic schedules for r irregularly occurring event

Consider r irregular polygons with vertices on some circle. Authors explains how the polygons should be arranged to minimize some criterion function depending on the distances between adjacent vertices. A solution of this problem is given. It is based on a decomposition of the set of all schedules into local regions in which the optimization problem is convex. For the criterion functions minimize the maximum distance and maximize the minimum distance the local optimization problems are related to network flow problems which can be solved efficiently. If the sum of squared distances is to be minimized a locally optimal solution can be found by solving a system of linear equations. For fixed r the global problem is polynomially solvable for all the above-mentioned objective functions. In the general case, however, the global problem is NP-hard