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Triangle enumeration is a fundamental problem in large-scale graph analysis. For instance, triangles are used to solve practical problems like community detection and spam filtering. On the other hand, there is a large amount of data stored on database management systems (DBMSs), which can be modeled and analyzed as graphs. Alternatively, graph data can be quickly loaded into a DBMS. Our paper shows how to adapt and optimize a randomized distributed triangle enumeration algorithm with SQL queries, which is a significantly different approach from programming graph algorithms in traditional languages such as Python or C++. We choose a parallel columnar DBMS given its fast query processing, but our solution should work for a row DBMS as well. Our randomized solution provides a balanced workload for parallel query processing, being robust to the existence of skewed degree vertices. We experimentally prove our solution ensures a balanced data distribution, and hence workload, among machines. The key idea behind the algorithm is to evenly partition all possible triplets of vertices among machines, sending edges that may form a triangle to a proxy machine; this edge redistribution eliminates shuffling edges during join computation and therefore triangle enumeration becomes local and fully parallel. In summary, our algorithm exhibits linear speedup with large graphs, including graphs that have high skewness in vertex degree distributions. 

The title three-dimensional metal–organic framework (MOF) compound, {(NH 4 ) 2 [Zn 2 (C 9 H 3 O 6 ) 2 ]·2C 5 H 9 NO} n , features an anionic framework constructed from Zn 2+ cations and benzene-1,3,5-tricarboxylate (BTC) organic anions. Charge balance is achieved by outer sphere ammonium cations formed by degradation of di- n -butylamine in the solvothermal synthesis of the compound. Binuclear {Zn 2 (COO) 2 } entities act as the framework's secondary building units. Each Zn II atom has a tetrahedral coordination environment with an O 4 set of donor atoms. The three-dimensional framework adopts a rutile-type topology and channels are filled in an alternating fashion with ordered and disordered 1-methylpyrrolidin-2-one solvent molecules and ammonium cations. The latter are held in the channels via four N—H...O hydrogen bonds, including three with the benzene-1,3,5-tricarboxylate ligands of the anionic framework and one with a 1-methylpyrrolidin-2-one solvent molecule. 

In the title compound, C 12 H 13 NO 2 , the five-membered ring has an envelope conformation; the disubstituted C atom lies out of the mean plane through the four other ring atoms (r.m.s. deviation = 0.0038 Å) by 0.1877 (18) Å. The plane of the phenyl substituent is practically perpendicular to that of the planar part of the five-membered ring, with a dihedral angle of 87.01 (5)°. In the crystal, molecules are linked by weak C—H...O hydrogen bonds, forming inversion dimers. The dimers are linked by further C—H...O hydrogen bonds, as well as carbonyl–carbonyl attractive interactions [O...C = 3.2879 (19) Å], forming a three-dimensional framework structure.