In this paper, we present an update to our previous submission from Graph Challenge 2017. This work describes and evaluates new software algorithm optimizations undertaken for our 2018 year submission on Collaborative CPU+GPU Algorithms for Triangle Counting and Truss Decomposition. First, we describe four major optimizations for the triangle counting which improved performance by up to 117x over our prior submission. Additionally, we show that our triangle-counting algorithm is on average 151.7x faster than NVIDIA’s NVGraph library (max 476x) for SNAP datasets. Second, we propose a novel parallel k-truss decomposition algorithm that is time-efficient and is up to 13.9x faster than our previous submission. Third, we evaluate the effect of generational hardware improvements between the IBM “Minsky” (POWER8, P100, NVLink 1.0) and “Newell” (POWER9, V100, NVLink 2.0) platforms. Lastly, the software optimizations presented in this work and the hardware improvements in the Newell platform enable analytics and discovery on large graphs with millions of nodes and billions of edges in less than a minute. In sum, the new algorithmic implementations are significantly faster and can handle much larger “big” graphs.