@misc{BertholdHeinzSchulz, author = {Berthold, Timo and Heinz, Stefan and Schulz, Jens}, title = {An approximative Criterion for the Potential of Energetic Reasoning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12655}, number = {11-12}, abstract = {Energetic reasoning is one of the most powerful propagation algorithms in cumulative scheduling. In practice, however, it is not commonly used because it has a high running time and its success highly depends on the tightness of the variable bounds. In order to speed up energetic reasoning, we provide an easy-to-check necessary condition for energetic reasoning to detect infeasibilities. We present an implementation of energetic reasoning that employs this condition and that can be parametrically adjusted to handle the trade-off between solving time and propagation overhead. Computational results on instances from the PSPLIB are provided. These results show that using this condition decreases the running time by more than a half, although more search nodes need to be explored.}, language = {en} } @misc{HeinzSchulz, author = {Heinz, Stefan and Schulz, Jens}, title = {Explanations for the Cumulative Constraint: an Experimental Study}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12668}, number = {11-13}, abstract = {In cumulative scheduling, conflict analysis seems to be one of the key ingredients to solve such problems efficiently. Thereby, the computational complexity of explanation algorithms plays an important role. Even more when we are faced with a backtracking system where explanations need to be constructed on the fly. In this paper we present extensive computational results to analyze the impact of explanation algorithms for the cumulative constraint in a backward checking system. The considered explanation algorithms differ in their quality and computational complexity. We present results for the domain propagation algorithms time-tabling, edge-finding, and energetic reasoning.}, language = {en} } @inproceedings{BertholdHeinzSchulz, author = {Berthold, Timo and Heinz, Stefan and Schulz, Jens}, title = {An approximative Criterion for the Potential of Energetic Reasoning}, series = {Theory and Practice of Algorithms in (Computer) Systems}, volume = {6595}, booktitle = {Theory and Practice of Algorithms in (Computer) Systems}, pages = {229 -- 239}, language = {en} } @inproceedings{HeinzSchulz, author = {Heinz, Stefan and Schulz, Jens}, title = {Explanations for the Cumulative Constraint: An Experimental Study}, series = {Experimental Algorithms}, volume = {6630}, booktitle = {Experimental Algorithms}, pages = {400 -- 409}, language = {en} }