The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms are known, but for the general case truly subquadratic algorithms remain elusive. Our first result is a reduction from the Orthogonal Vectors problem to Sub...

Employing higher-order subtree structures in graph-based dependency parsing has shown substantial improvement over the accuracy, however suffers from the inefficiency increasing with the order of subtrees. We present a new reranking approach for dependency parsing that can utilize complex subtree representation by applying efficient subtree selection heuristics. We demonstrate the effectiveness...

We study the subtree isomorphism problem: Given trees H and G, find a subtree of G which is isomorphic to H or decide that there is no such subtree. We give an O( k1:5 logkn)time algorithm for this problem, where k and n are the number of vertices in H and G respectively. This improves over the O(k1:5n) algorithms of Chung and Matula. We also give a randomized (Las Vegas) O(min(k1:45n; kn1:43))...

The tree-shaped facility location problem aims to locate a subtree on the center of a given tree network. This paper deals with four types of the problems in which the centrality for a subtree is measured by the eccentricity or the distance-sum, and a subtree may contain partial edges or not. We investigate the relationship between these problems and knapsack-type problems. The relation leads t...

Mining frequent subtrees from databases of labeled trees is a new research field that has many practical applications in areas such as computer networks, Web mining, bioinformatics, XML document mining, etc. These applications share a requirement for the more expressive power of labeled trees to capture the complex relations among data entities. Although frequent subtree mining is a more diffic...

We propose a novel source-side dependency tree reordering model for statistical machine translation, in which subtree movements and constraints are represented as reordering events associated with the widely used lexicalized reordering models. This model allows us to not only efficiently capture the statistical distribution of the subtree-to-subtree transitions in training data, but also utiliz...

Graph kernels have become a well-established approach in graph mining. One of the early graph kernels, the frequent subgraph kernel, is based on embedding the graphs into a feature space spanned by the set of all frequent connected subgraphs in the input graph database. A drawback of this graph kernel is that the preprocessing step of generating all frequent connected subgraphs is computational...

Given a collection of leaf-labeled trees on a common leafset and a fraction f in (1/2,1], a frequent subtree (FST) is a subtree isomorphically included in at least fraction f of the input trees. The well-known maximum agreement subtree (MAST) problem identifies FST with f = 1 and having the largest number of leaves. Apart from its intrinsic interest from the algorithmic perspective, MAST has pr...

). In this note we provide another bijection, which is simpler. Furthermore, it preserves more of the structure of the tree. The basic idea is that, when • ◦ is forbidden, any sequence of nodes connected by right edges must have labels white . . . white, followed by black . . . black. We translate the restricted 2-binary tree recursively into a ternary tree from the root to the leaves, by leavi...

We show that for every rooted, finitely branching, pruned tree T of height ω there exists a family F which consists of order isomorphic to T subtrees of the dyadic tree C = {0, 1}<N with the following properties: (i) the family F is a Gδ subset of 2C ; (ii) every perfect subtree of C contains a member of F ; (iii) if K is an analytic subset of F , then for every perfect subtree S of C there exi...