Recomputation algorithms collectively refer to a family of methods that aims to reduce the memory consumption of the backpropagation by selectively discarding the intermediate results of the forward propagation and recomputing the discarded results as needed. In this paper, we will propose a novel and efficient recomputation method that can be applied to a wider range of neural nets than previous methods. We use the language of graph theory to formalize the general recomputation problem of minimizing the computational overhead under a fixed memory budget constraint, and provide a dynamic programming solution to the problem. Our method can reduce the peak memory consumption on various benchmark networks by $36\%\sim81\%$, which outperforms the reduction achieved by other methods.

Similarity join finds all pairs of objects (i, j) with similarity score s(i, j) greater than some specified threshold θ. This is a fundamental query problem in the database research community, and is used in many practical applications, such as duplicate detection, merge/purge, record linkage, object matching, and reference conciliation. In this paper, we propose a scalable approximation algorithm with an arbitrary accuracy for the similarity join problem with the SimRank similarity measure. The algorithm consists of two phases: filter and verification. The filter phase enumerates similar pair candidates, and the similarity of each candidate is then assessed in the verification phase. The scalability of the proposed algorithm is experimentally verified for large real networks. The complexity depends only on the number of similar pairs, but does not depend on all pairs O(n2). The proposed algorithm scales up to the network of 5M vertices and 70M edges. By comparing the state-of-the-art algorithms, it is about 10 times faster and it requires about 10 times smaller memory.

SimRank, proposed by Jeh and Widom, provides a good similarity measure that has been successfully used in numerous applications.While there are many algorithms proposed for computing SimRank, their computational costs are very high.In this paper, we propose a new computational technique, "SimRank linearization," for computing SimRank, which converts the SimRank problem to a linear equation problem.By using this technique, we can solve many SimRank problems, such as single-pair compuation, single-source computation, all-pairs computation, top k searching, and similarity join problems, efficiently.

SimRank, proposed by Jeh and Widom, provides a good similarity score and has been successfully used in many of the above mentioned applications. While there are many algorithms proposed so far to compute SimRank, but unfortunately, none of them are scalable up to graphs of billions size. Motivated by this fact, we consider the following SimRank-based similarity search problem: given a query vertex u, find top-k vertices v with the k highest SimRank scores s(u,v) with respect to u.