A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic embeddings of a query hypergraph in a data hypergraph, is one of the fundamental problems. In this paper, we present a novel algorithm for hypergraph pattern matching by introducing (1) the intersection constraint, a necessary and sufficient condition for valid embeddings, which significantly speeds up the verification process, (2) the candidate hyperedge space, a data structure that stores potential mappings between hyperedges in the query hypergraph and the data hypergraph, and (3) the Match-and-Filter framework, which interleaves matching and filtering operations to maintain only compatible candidates in the candidate hyperedge space during backtracking. Experimental results on real-world datasets demonstrate that our algorithm significantly outperforms the state-of-the-art algorithms, by up to orders of magnitude in terms of query processing time.

Subgraph counting is a fundamental problem in understanding and analyzing graph structured data, yet computationally challenging. This calls for an accurate and efficient algorithm for Subgraph Cardinality Estimation, which is to estimate the number of all isomorphic embeddings of a query graph in a data graph. We present FaST est , a novel algorithm that combines (1) a powerful filtering technique to significantly reduce the sample space, (2) an adaptive tree sampling algorithm for accurate and efficient estimation, and (3) a worst-case optimal stratified graph sampling algorithm for hard instances. Extensive experiments on real-world datasets show that FaST est outperforms state-of-the-art sampling-based methods by up to two orders of magnitude and GNN-based methods by up to three orders of magnitude in terms of accuracy.

In this paper we present a homomorphic computation algorithm that finds an optimal local alignment of a pair of encrypted sequences, based on the Smith-Waterman recurrence. Our algorithm also includes an efficient method of finding the location of an optimal local alignment, in order to avoid costly conditional branching in the backtracking. To reduce computation time, we use two level parallel computations: one for filling the entries of the dynamic programming recurrence, and the other for implementing the circuits. To the best of our knowledge, this is the first attempt to compute an optimal local alignment of homomorphically encrypted sequences. With the efficient location retrieval, parallel computations, and a proper HE scheme, our implementation shows good performances in the experiment so as to be useful in practice.