Efficient Computation of Subspace Skyline over Categorical Domains

Platforms such as AirBnB, Zillow, Yelp, and related sites have transformed the way we search for accommodation, restaurants, etc. The underlying datasets in such applications have numerous attributes that are mostly Boolean or Categorical. Discovering the skyline of such datasets over a subset of attributes would identify entries that stand out while enabling numerous applications. There are only a few algorithms designed to compute the skyline over categorical attributes, yet are applicable only when the number of attributes is small. In this paper, we place the problem of skyline discovery over categorical attributes into perspective and design efficient algorithms for two cases. (i) In the absence of indices, we propose two algorithms, ST-S and ST-P, that exploits the categorical characteristics of the datasets, organizing tuples in a tree data structure, supporting efficient dominance tests over the candidate set. (ii) We then consider the existence of widely used precomputed sorted lists. After discussing several approaches, and studying their limitations, we propose TA-SKY, a novel threshold style algorithm that utilizes sorted lists. Moreover, we further optimize TA-SKY and explore its progressive nature, making it suitable for applications with strict interactive requirements. In addition to the extensive theoretical analysis of the proposed algorithms, we conduct a comprehensive experimental evaluation of the combination of real (including the entire AirBnB data collection) and synthetic datasets to study the practicality of the proposed algorithms. The results showcase the superior performance of our techniques, outperforming applicable approaches by orders of magnitude

Efficient Process-to-Node Mapping Algorithms for Stencil Computations

Good process-to-compute-node mappings can be decisive for well performing HPC applications. A special, important class of process-to-node mapping problems is the problem of mapping processes that communicate in a sparse stencil pattern to Cartesian grids. By thoroughly exploiting the inherently present structure in this type of problem, we devise three novel distributed algorithms that are able to handle arbitrary stencil communication patterns effectively. We analyze the expected performance of our algorithms based on an abstract model of inter- and intra-node communication. An extensive experimental evaluation on several HPC machines shows that our algorithms are up to two orders of magnitude faster in running time than a (sequential) high-quality general graph mapping tool, while obtaining similar results in communication performance. Furthermore, our algorithms also achieve significantly better mapping quality compared to previous state-of-the-art Cartesian grid mapping algorithms. This results in up to a threefold performance improvement of an MPI_Neighbor_alltoall exchange operation. Our new algorithms can be used to implement the MPI_Cart_create functionality.Comment: 18 pages, 9 Figure

Local Strategy Improvement for Parity Game Solving

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy improvement algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present a local strategy improvement algorithm which explores the game graph on-the-fly whilst performing the improvement steps. We also compare it empirically with existing global strategy improvement algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy improvement can outperform these others by several orders of magnitude