Runtime prediction of real programs on real machines

Algorithms are more and more made available as part of libraries or tool kits. For a user of such a library statements of asymptotic running times are almost meaningless as he has no way to estimate the constants involved. To choose the right algorithm for the targeted problem size and the available hardware, knowledge about these constants is important. Methods to determine the constants based on regression analysis or operation counting are not practicable in the general case due to inaccuracy and costs respectively. We present a new general method to determine the implementation and hardware specific running time constants for combinatorial algorithms. This method requires no changes of the implementation of the investigated algorithm and is applicable to a wide range of of programming languages. Only some additional code is necessary. The determined constants are correct within a constant factor which depends only on the hardware platform. As an example the constants of an implementation of a hierarchy of algorithms and data structures are determined. The hierarchy consists of an algorithm for the maximum weighted bipartite matching problem (MWBM), Dijkstra's algorithm, a Fibonacci heap and a graph representation based on adjacency lists. ion frequencies are at most 50 \% on the tested hardware platforms

Factors Influencing Consumer Behavior to Purchase Sustainable Cosmetic Products in a German Context

In today's markets, corporate social responsibility is a new consumer expectation. Organizations across all industries are trying to meet these expectations by building a positive reputation and sending a signal to their stakeholders. However, consumers’ environmental behavior is not always the result of their positive attitudes towards environmental issues. Potentially, their environmentally friendly attitudes are contradicted by their actual behavior. This means that people, who have positive attitudes about sustainable products and state that they would purchase them, may not actually buy them after all. In addition, consumers often do not wish to spend more money on buying sustainably, even if they have higher expectations towards sustainable products or companies. Further research is therefore needed to explain the gap between consumer awareness and actual purchasing behavior. In several contexts, environmentally friendly consumption, called sustainable consumption, has been explained by the theory of planned behavior (TPB), such as when buying food or apparel. Sustainable consumption often results from planned decisions rather than hedonic reasons.        &nbsp

A Planarity Test via Construction Sequences

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise

Spin polarization of the Ar* 2p−11/2 4s and 2p−11/2 3d resonant Auger decay

The spin-resolved Auger decay of the Ar 2p−11/2 3d state was measured at moderate energy resolution and compared with the decay of the 2p−11/2 4s. The former shows a lower transferred spin polarization and a similar, if not higher, dynamical spin polarization, supporting the statement that a fully resolved spectrum is not a necessary condition for observing dynamical spin polarization. An interpretation of the spin polarization as configuration interaction induced effect in the final ionic state leads to partial agreement with our relativistic distorted wave calculation utilizing a 36 configuration state function basis set. Comparison of the experimental and numerical results leads to ambiguities for at least one Auger line. A hypothetical, qualitative interpretation is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58121/2/b7_17_012.pd

Quantitative Coding and Complexity Theory of Compact Metric Spaces

Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is usually straightforward and/or complexity-theoretically inessential (up to polynomial time, say); but concerning continuous data, already real numbers naturally suggest various encodings with very different computational properties. With respect to qualitative computability, Kreitz and Weihrauch (1985) had identified ADMISSIBILITY as crucial property for 'reasonable' encodings over the Cantor space of infinite binary sequences, so-called representations [doi:10.1007/11780342_48]: For (precisely) these does the sometimes so-called MAIN THEOREM apply, characterizing continuity of functions in terms of continuous realizers. We rephrase qualitative admissibility as continuity of both the representation and its multivalued inverse, adopting from [doi:10.4115/jla.2013.5.7] a notion of sequential continuity for multifunctions. This suggests its quantitative refinement as criterion for representations suitable for complexity investigations. Higher-type complexity is captured by replacing Cantor's as ground space with Baire or any other (compact) ULTRAmetric space: a quantitative counterpart to equilogical spaces in computability [doi:10.1016/j.tcs.2003.11.012]

Partitioning Graphs to Speed Up Dijkstra's Algorithm

In this paper, we consider Dijkstra's algorithm for the point-to-point shortest path problem in large and sparse graphs with a given layout. Lauther presented a method that uses a partitioning of the graph to perform a preprocessing which allows to speed-up Dijkstra's algorithm considerably. We present an experimental study that evaluates which partitioning methods are suited for this approach. In particular, we examine partitioning algorithms from computational geometry and compare their impact on the speed-up of the shortest-path algorithm. Using a suited partitioning algorithm speed-up factors of 500 and more were achieved. Furthermore, we present an extension of this speed-up technique to multiple levels of partitionings. With this multi-level variant, the same speed-up factors can be achieved with smaller space requirements. It can therefore be seen as a compression of the precomputed data that conserves the correctness of the computed shortest paths