27133006
Binary partition based algorithms for mining association rules
Mining association rules is an important data mining problem. A fast binary partition-based algorithm (BPA) for mining association rules in large databases is presented in this paper. Basically, the framework of BPA is similar to that of the algorithm Apriori. In the first pass, all the frequent 1-item sets are divided into two disjoint parts. Accordingly, in each subsequent pass k, we partition the set of all the frequent k-item sets into three subsets. Any two different partitions are disjoint. If necessary, this partitioning procedure can be a recursive one. Therefore, we get a binary partition tree in the first pass and a corresponding ternary partition tree in each subsequent pass k. Due to such a partition, BPA can be very easily parallelized, assuming a shared-memory architecture.
30099215
Indexing and incremental updating condensed data cube
OLAP (online analytical processing) servers usually pre-compute data cubes to improve the response time of possible aggregate queries over cuboids with different grouping attributes. To reduce the huge size of a sparse data cube, the base single tuples (BSTs) are explored to condense cube tuples aggregated from the same set of source tuples into one tuple, whenever such condensing will not require further aggregate when the cube is used to answer queries. We propose the CuboidTree to index the BST condensed cube. Using both synthetic and real world data, we conducted experiments to demonstrate query processing and bulk incremental updating performance of the indexing scheme.
44503656
s-Regular cubic graphs as coverings of the complete bipartite graph K3, 3
2486014
On vertex-transitive graphs of odd prime-power order
Marusic (Ann. Discrete Math. 27 (1985) 115) proved that all vertex-transitive graphs of order pk are Cayley graphs for each prime p and k = 1,2, or 3, and constructed a non-Cayley vertex-transitive graph of order pk and valency 2p + 2 for each prime p ≥ 5 and k ≥ 4. McKay and Praeger (J. Austral. Math. Soc. (A) 56 (1994) 53) gave an alternative construction of a non-Cayley vertex-transitive graph of order pk for each prime p ≥ 3 and k ≥ 4. In this paper it is proved that, for each positive integer k and each prime p ≥ 3, a vertex-transitive graph of order pk with valency less than 2p + 2 is a Cayley graph.
11331203
Automorphism groups of Cayley graphs on symmetric groups with generating transposition sets
Let T be a set of transpositions of the symmetric group Sn. The transposition graph Tra(T) of T is the graph with vertex set {1, 2, ..., n} and edge set {ij|(i j) ∈ T}. In this paper it is shown that if n ≥ 3, then the automorphism group of the transposition graph Tra(T) is isomorphic to Aut(Sn, T) = {α ∈ Aut(Sn)|Tα = T} and if T is a minimal generating set of Sn then the automorphism group of the Cayley graph Cay(Sn, T) is the semiproduct R(Sn) Aut(Sn, T), where R(Sn) is the right regular representation of Sn. As a result, we generalize a theorem of Godsil and Royle [C.D. Godsil, G. Royle, Algebraic Graph Theory, Springer, New York, 2001, p. 53] regarding the automorphism groups of Cayley graphs on Sn : if T is a minimal generating set of Sn and the automorphism group of the transposition graph Tra(T) is trivial then the automorphism group of the Cayley graph Cay(Sn, T) is isomorphic to Sn.
207795841
Automorphism groups of tetravalent Cayley graphs on regular p-groups
Let Cay(G,S) be a connected tetravalent Cayley graph on a regular p-group G and let Aut(G) be the automorphism group of G. In this paper, it is proved that, for each prime p 2,5, the automorphism group of the Cayley graph Cay(G,S) is the semidirect product R(G)@?Aut(G,S) where R(G) is the right regular representation of G and Aut(G,S)={@[email protected]?Aut(G)|S^@a=S}. The proof depends on the classification of finite simple groups. This implies that if p 2,5 then the Cayley graph Cay(G,S) is normal, namely, the automorphism group of Cay(G,S) contains R(G) as a normal subgroup.
1503799
Deza digraphs
We consider a directed version of Deza graphs. A digraph is said to be a Deza digraph if it is regular and the number of common out-neighbors of any two distinct vertices takes on at most two values. We introduce some constructions and develop some basic theory. In particular, constructions from Cayley digraphs, graph lexicograph products and graph directed products are described. Moreover, we characterize a family of normal Deza digraphs, and list all cyclic strictly Deza digraphs with at most six vertices. Finally, connections to weakly distance-regular digraphs are discussed, and all strictly Deza digraphs which are also weakly distance-regular digraphs with at most ten vertices are listed.