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A multi-tenant database system for Software as a Service (SaaS) should offer schemas that are flexible in that they can be extended for different versions of the application and dynamically modified while the system is on-line. This paper presents an experimental comparison of five techniques for implementing flexible schemas for SaaS. In three of these techniques, the database "owns" the schema in that its structure is explicitly defined in DDL. Included here is the commonly-used mapping where each tenant is given their own private tables, which we take as the baseline, and a mapping that employs Sparse Columns in Microsoft SQL Server. These techniques perform well, however they offer only limited support for schema evolution in the presence of existing data. Moreover they do not scale beyond a certain level. In the other two techniques, the application "owns" the schema in that it is mapped into generic structures in the database. Included here are XML in DB2 and Pivot Tables in HBase. These techniques give the application complete control over schema evolution, however they can produce a significant decrease in performance. We conclude that the ideal database for SaaS has not yet been developed and offer some suggestions as to how it should be designed.

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MSC:15A18 05C50 05C85 Keywords: Threshold graph Adjacency matrix Eigenvalue EnergyAssuming a uniform random model of selecting creation sequences, we show that almost every connected threshold graph has more negative than positive eigenvalues. We show that no threshold graphs have eigenvalues in (−1, 0). Sequences of equienergetic graphs are given including the striking result that for all n ≥ 3, there exist n − 1 threshold graphs of order n 2 , pairwise noncospectral, each equienergetic to K n 2 . For all n > 8, we find an n-vertex hyperenergetic threshold graph.