Multiway spatial joins are a commonly occurring and fundamental type of query for spatial data processing. This article presents models and algorithms to schedule this type of query in distributed database systems while attempting to strike a balance between makespan and communication costs. We propose three algorithms based on combinatorial optimization methods: the well-known linear relaxation technique of rounding a solution generated by linear programming (LP), a more sophisticated Lagrangian Relaxation method (LR), as well as a greedy heuristic (GR) for baseline comparison. Our evaluation shows that a schedule built using GR consumes, on average, 22% more processing and communication resources than a more elaborate schedule constructed via the LR method, when scheduling a query for 64 machines. The schedule provided by LR is also, on average, an order of magnitude closer to the optimal schedule for a query compared to GR. We show that scheduling Gigabyte-size multiway queries before execution can reduce its processing time by an order of magnitude compared to state-of-the-art frameworks for spatial data processing that do not have this capability, and can significantly reduce the amount of shuffled data in the network.

The solution space of an optimization problem consists of all its feasible solutions. In this work, we present a systematic literature review on the application of Information Visualization (IV) techniques for understanding and exploring such solution spaces. The review was conducted on several search databases, and we identified 264 papers that satisfied our inclusion criteria. A performance filter was applied to these papers, and we further analyzed and extracted data from 65 of them. Our analysis shows that there are a variety of solution space visualization approaches and provides useful references to support further studies on the subject.

BACKGROUND: Phylogenetic comparative analyses usually rely on a single consensus phylogenetic tree in order to study evolutionary processes. However, most phylogenetic trees are incomplete with regard to species sampling, which may critically compromise analyses. Some approaches have been proposed to integrate non-molecular phylogenetic information into incomplete molecular phylogenies. An expanded tree approach consists of adding missing species to random locations within their clade. The information contained in the topology of the resulting expanded trees can be captured by the pairwise phylogenetic distance between species and stored in a matrix for further statistical analysis. Thus, the random expansion and processing of multiple phylogenetic trees can be used to estimate the phylogenetic uncertainty through a simulation procedure. Because of the computational burden required, unless this procedure is efficiently implemented, the analyses are of limited applicability. RESULTS: In this paper, we present efficient algorithms and implementations for randomly expanding and processing phylogenetic trees so that simulations involved in comparative phylogenetic analysis with uncertainty can be conducted in a reasonable time. We propose algorithms for both randomly expanding trees and calculating distance matrices. We made available the source code, which was written in the C++ language. The code may be used as a standalone program or as a shared object in the R system. The software can also be used as a web service through the link: http://purl.oclc.org/NET/sunplin/. CONCLUSION: We compare our implementations to similar solutions and show that significant performance gains can be obtained. Our results open up the possibility of accounting for phylogenetic uncertainty in evolutionary and ecological analyses of large datasets.