With XML becoming a ubiquitous language for data interoperability purposes in multiple domains, efficient query of XML data is a critical problem. This has led to the design of algebraic frames based on tree-like patterns similar to the XML tree-structured data model. Tree patterns are graphical representations of queries about the data trees. They are actually compared to an input data tree to answer a query. Since the beginning of the 21st century, an astounding research effort has focused on tree pattern patterns and coincident optimization (a primary issue).