Frequent Hypergraph Mining

Abstract

The class of frequent hypergraph mining problems is introduced which includes the frequent graph mining problem class and contains also the frequent itemset mining problem. We study the computational properties of different problems belonging to this class. In particular, besides negative results, we present practically relevant problems that can be solved in incremental-polynomial time. Some of our practical algorithms are obtained by reductions to frequent graph mining and itemset mining problems. Our experimental results in the domain of citation analysis show the potential of the framework on problems that have no natural representation as an ordinary graph.

Efficient Graph Sequence Mining Using Reverse Search

“…11 is used, and GTRACE-RS is equivalent to gSpan [21]. The problem of enumerating all frequent and connected subgraphs cannot be solved in time that is polynomial in the output, which is a class of algorithms that find all patterns in polynomial time both in the total input size and the number of patterns, unless P = NP [2], [11]. Therefore, the problem addressed in this paper cannot be solved in time that is polynomial in the output.…”

Frequent subgraph mining in outerplanar graphs

“…We also note that, in contrast to incremental polynomial time, an output polynomial time algorithm may have in worst-case a delay time exponential in the size of the input before printing the th element for any ≥ 1. Although several algorithms mining frequent connected subgraphs from arbitrary graphs with respect to subgraph isomorphism have demonstrated their performance empirically (see, also, Section 4 below), we note that, unless P = NP, this general problem cannot be solved in output polynomial time [18] (i.e., in the most liberal class in the above hierarchy). On the other hand, the frequent graph mining problem is solvable in incremental polynomial time when the graphs in the dataset are restricted to forests and the patterns to trees.…”

“…There is a huge literature on this problem setting; an exhaustive overview of all related results on this problem goes beyond the scope of this paper. Since most of the related approaches allow arbitrary transaction graphs and use ordinary subgraph isomorphism as embedding operator, they deal with a computationally intractable task [18], and resort therefore to various heuristics. Below we briefly overview three types of heuristics appearing in the algorithms.…”

“…While the frequent pattern mining problem for trees is tractable (i.e., can be solved in incremental polynomial time; see [6] for an overview on frequent subtree mining), for arbitrary graphs it becomes intractable [18] (i.e., cannot even be solved in output polynomial time). Existing approaches to frequent pattern discovery for graphs have therefore resorted to various heuristic strategies and restrictions of the search space (see, e.g., [3,6,8,9,20,23,24,29,31,41]), but have not identified a practically relevant tractable graph class beyond trees.…”

FRISSMiner: Mining Frequent Graph Sequence Patterns Induced by Vertices

“…10, and increases exponentially when the average number of vertices in the union graphs increases or the minimum support threshold decreases. The problem of enumerating all frequent, connected, and induced subgraph patterns cannot be solved in time that is polynomial in the output, which is a class of algorithms that find all patterns in polynomial time both in the total input size and the number of patterns, unless P = NP [1], [18]. On the other hand, the complexity of the original PrefixSpan is polynomial delay, which is a class for which the maximum computation time between two consecutive outputs is bounded by a polynomial in the total input size [1].…”