Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

On parallel versus sequential approximation

In this paper we deal with the class NCX of NP Optimization problems that are approximable within constant ratio in NC. This class is the parallel counterpart of the class APX. Our main motivation here is to reduce the study of sequential and parallel approximability to the same framework. To this aim, we first introduce a new kind of NC-reduction that preserves the relative error of the approximate solutions and show that the class NCX has {em complete} problems under this reducibility. An important subset of NCX is the class MAXSNP, we show that MAXSNP-complete problems have a threshold on the parallel approximation ratio that is, there are positive constants $epsilon_1$, $epsilon_2$ such that although the problem can be approximated in P within $epsilon_1$ it cannot be approximated in NC within epsilon_2$, unless P=NC. This result is attained by showing that the problem of approximating the value obtained through a non-oblivious local search algorithm is P-complete, for some values of the approximation ratio. Finally, we show that approximating through non-oblivious local search is in average NC.Postprint (published version

Frequency-splitting Dynamic MRI Reconstruction using Multi-scale 3D Convolutional Sparse Coding and Automatic Parameter Selection

Department of Computer Science and EngineeringIn this thesis, we propose a novel image reconstruction algorithm using multi-scale 3D con- volutional sparse coding and a spectral decomposition technique for highly undersampled dy- namic Magnetic Resonance Imaging (MRI) data. The proposed method recovers high-frequency information using a shared 3D convolution-based dictionary built progressively during the re- construction process in an unsupervised manner, while low-frequency information is recovered using a total variation-based energy minimization method that leverages temporal coherence in dynamic MRI. Additionally, the proposed 3D dictionary is built across three different scales to more efficiently adapt to various feature sizes, and elastic net regularization is employed to promote a better approximation to the sparse input data. Furthermore, the computational com- plexity of each component in our iterative method is analyzed. We also propose an automatic parameter selection technique based on a genetic algorithm to find optimal parameters for our numerical solver which is a variant of the alternating direction method of multipliers (ADMM). We demonstrate the performance of our method by comparing it with state-of-the-art methods on 15 single-coil cardiac, 7 single-coil DCE, and a multi-coil brain MRI datasets at different sampling rates (12.5%, 25% and 50%). The results show that our method significantly outper- forms the other state-of-the-art methods in reconstruction quality with a comparable running time and is resilient to noise.ope