Discovery of association rules is an important data mining task. Several algorithms have been proposed to solve this problem. Most of them require repeated passes over the database, which incurs huge I/O overhead and high synchronization expense in parallel cases. There are a few algorithms trying to reduce these costs. But they contain weaknesses such as often requiring high pre-processing cost to get a vertical database layout, containing much redundant computation in parallel cases, and so on. We propose new association mining algorithms to overcome the above drawbacks, through minimizing the I/O cost and effectively controlling the computation cost. Experiments on well-known synthetic data show that our algorithms consistently outperform a priori, one of the best algorithms for association mining, by factors ranging from 2 to 4 in most cases. Also, our algorithms are very easy to be parallelized, and we present a parallelization for them based on a shared-nothing architecture. We observe that our parallelization develops the parallelism more sufficiently than two of the best existing parallel algorithms.