Market partitioning and the geometry of the resource space

This article gives a new explanation for generalist and specialist organizations' coexistence in crowded markets. It addresses organizational ecology's resource-partitioning theory, which explains market histories with scale economies and crowding, and it shows that some main predictions of this theory can be restated in terms of structural properties of the N-dimensional Euclidean space. As resource-space dimensionality increases, the changing niche configurations open opportunities for specialists. The proposed approach draws upon the sphere-packing problem in geometry. The model also explains new observations, and its findings apply to a range of crowding and network models in sociology.</p

The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematic

Algorithms for visualization of graph-based structures

Buildings today are built to maintain a healthy indoor environment and an efficient energy usage which is probably why damages caused by dampness has increased since the 1960’s. A study between year 2008 and 2010 showed that 26 percent of the 110 000 examined houses had damages and flaws caused by dampness that could prove to be harmful later on. This means that one out of four bathrooms risk the chance to develop damages by dampness. Approximately 2 percent of the houses had already developed water damages. It is here where the problems appear. A house or a building that is damaged by water of dampness need time to dry out before any renovation can take place. This means that damaged parts must be removed and allowed to dry out, this takes a long time to do and the costs are high and at the same time it can cause inconvenience to the residents. Here is where the Air Gap Method enters the picture. The meaning with the method is to drain and dry out the moisture without the need to perform a larger renovation. The Air Gap Method is a so called "forgiving"-system that is if water damages occur the consequences will be small. The Air Gap method means that an air gap is created in the walls, ceiling and the floor where a heating cable in the gap heats up the air and creates an air movement. The point is to create a stack effect in the gap that with the help of the air movement transports the damp air through an opening by the ceiling. The aim of this thesis is to examine if it’s necessary with the heating cable in the air gap and if there is a specific drying out pattern of the water damaged bathroom floor. The possibility of mould growth will also be examined. The study showed that the damped floor did dry out even without a heating cable, but as one of the studies showed signs of mould growth it is shown that the risk for mould growth is higher without a heating cable. There was a seven days difference in the drying out time between the studies with and without the heating cable; this difference can be decisive for mould growth which is why the heating cable is recommended. The Air Gap method is quite easy to apply in houses with light frame constructions simply by using a smaller dimension on the studs to create the air gap in the floor and walls. The method can also be applied in apartment buildings with a concrete frame by using the room-in- room principal. When renovating existing bathrooms it’s easier to use prefabricated elements to create the air gap in the floor and walls. ~

Timing-Driven Macro Placement

Placement is an important step in the process of finding physical layouts for electronic computer chips. The basic task during placement is to arrange the building blocks of the chip, the circuits, disjointly within a given chip area. Furthermore, such positions should result in short circuit interconnections which can be routed easily and which ensure all signals arrive in time. This dissertation mostly focuses on macros, the largest circuits on a chip. In order to optimize timing characteristics during macro placement, we propose a new optimistic timing model based on geometric distance constraints. This model can be computed and evaluated efficiently in order to predict timing traits accurately in practice. Packing rectangles disjointly remains strongly NP-hard under slack maximization in our timing model. Despite of this we develop an exact, linear time algorithm for special cases. The proposed timing model is incorporated into BonnMacro, the macro placement component of the BonnTools physical design optimization suite developed at the Research Institute for Discrete Mathematics. Using efficient formulations as mixed-integer programs we can legalize macros locally while optimizing timing. This results in the first timing-aware macro placement tool. In addition, we provide multiple enhancements for the partitioning-based standard circuit placement algorithm BonnPlace. We find a model of partitioning as minimum-cost flow problem that is provably as small as possible using which we can avoid running time intensive instances. Moreover we propose the new global placement flow Self-Stabilizing BonnPlace. This approach combines BonnPlace with a force-directed placement framework. It provides the flexibility to optimize the two involved objectives, routability and timing, directly during placement. The performance of our placement tools is confirmed on a large variety of academic benchmarks as well as real-world designs provided by our industrial partner IBM. We reduce running time of partitioning significantly and demonstrate that Self-Stabilizing BonnPlace finds easily routable placements for challenging designs – even when simultaneously optimizing timing objectives. BonnMacro and Self-Stabilizing BonnPlace can be combined to the first timing-driven mixed-size placement flow. This combination often finds placements with competitive timing traits and even outperforms solutions that have been determined manually by experienced designers

Organisational niche boundaries in the n-space

The paper investigates organizational boundary spanning from the point of view of neighborhood relations. Neighborhood is defined with the closeness of organizations' resource utilization patterns. The key resource is the clientele's demand for organizational outputs (products, party programs, membership, etc.). Demand is characterized qualitatively by n taste descriptors that span an n-dimensional resource space. Organizational niche boundaries may take different forms and size. To avoid niche overlap over boundaries, organizations can configure in the resource space in different clusterings. Which are the densest arrangements that allow for the coexistence of maximal number of organizations? How can these coexisting neighborhoods build up? How do competition, new entry and the number of immediate neighbors change around the niche boundary with space dimension? The paper applies results of the sphere packing problem in n-dimensional geometry to answer these questions.

High Multiplicity Strip Packing

In the two-dimensional high multiplicity strip packing problem (HMSPP), we are given k distinct rectangle types, where each rectangle type Ti has ni rectangles each with width 0 \u3c wi and height 0 \u3c hi The goal is to pack these rectangles into a strip of width 1, without rotating or overlapping the rectangles, such that the total height of the packing is minimized. Let OPT(I) be the optimal height of HMSPP on input I. In this thesis, we consider HMSPP for the case when k = 3 and present an OPT(I) + 5/3 polynomial time approximation algorithm for it. Additionally, we consider HMSPP for the case when k = 4 and present an OPT(I) + 5/2 polynomial time approximation algorithm for it