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Two vertices u, w ∈ V, vv-dominate each other if they are incident on the same block. A set S ⊆ V is a vv-dominating set (VVD-set) if every vertex in V – S is vv-dominated by a vertex in S. The vv-domination number γvv = γvv(G) is the cardinality of a minimum VVD-set of G. Two blocks b1, b2 ∈ B(G) the set of all blocks of G, bb-dominate each other if there is a common cutpoint. A set L ⊆ B(G) is said to be a bb-dominating set (BBD set) if every block in B(G) – L is bb-dominated by some block in L. The bb-domination number γbb = γbb(G) is the cardinality of a minimum BBD-set of G. A vertex v and a block b are said to b-dominate each other if v is incident on the block b. Then vb-domination number γvb = γvb(G) (bv-domination number γbv = γbv(G)) is the minimum number of vertices (blocks) needed to b-dominate all the blocks (vertices) of G. In this paper we study the properties of these block domination parameters and establish a relation between these parameters giving an inequality chain consisting of nine parameters.

There has been rapid growth in the field of graphical processing unit (GPU) programming due to the drastic increase in the computing hardware manufacturing. The technology used in these devices is now more affordable and accessible to the general public. With this growth, many serial programming applications that are now being transformed into more efficient parallel programming applications with significant improvement in the performance. The best example for this is parallel implementation of the probabilistic data structure Bloom filter in set membership queries. However, despite of it’s remarkable performance in speed and memory usage, there is a computational overhead in the calculation of hashes in Bloom filter. In this paper, the impact of the choice of hash functions on the qualitative properties of the Bloom filter has been experimentally recorded and the results show that there is a possibility of large performance gap among various hash functions. We have implemented the Bloom filter based pattern matching technique on GPU using compute unified device architecture (CUDA) and benchmark the performance of several cryptographic and non-cryptographic hash functions.