  The blooming availability of traces for social, biological, and communication
networks opens up unprecedented opportunities in analyzing diffusion processes
in networks. However, the sheer sizes of the nowadays networks raise serious
challenges in computational efficiency and scalability.
  In this paper, we propose a new hyper-graph sketching framework for inflence
dynamics in networks. The central of our sketching framework, called SKIS, is
an efficient importance sampling algorithm that returns only non-singular
reverse cascades in the network. Comparing to previously developed sketches
like RIS and SKIM, our sketch significantly enhances estimation quality while
substantially reducing processing time and memory-footprint. Further, we
present general strategies of using SKIS to enhance existing algorithms for
influence estimation and influence maximization which are motivated by
practical applications like viral marketing. Using SKIS, we design high-quality
influence oracle for seed sets with average estimation error up to 10x times
smaller than those using RIS and 6x times smaller than SKIM. In addition, our
influence maximization using SKIS substantially improves the quality of
solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x
memory reduction for the fastest RIS-based DSSA algorithm, while maintaining
the same theoretical guarantees.
