The Tree Inclusion Problem: In Linear Space and Faster

Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML databases. Kilpel\"ainen and Mannila [\emph{SIAM J. Comput. 1995}] presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when $P$ and $T$ have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. Let $n_S$, $l_S$, and $d_S$ denote the number of nodes, the number of leaves, and the %maximum depth of a tree $S \in \{P, T\}$. In this paper we show that the tree inclusion problem can be solved in space $O(n_T)$ and time: O(\min(l_Pn_T, l_Pl_T\log \log n_T + n_T, \frac{n_Pn_T}{\log n_T} + n_{T}\log n_{T})). This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.Comment: Minor updates from last tim

Evidence of clonal budding in a radial cluster of Paraconularia crustula (White) (Pennsylvanian: ?Cnidaria)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73153/1/j.1502-3931.1992.tb01645.x.pd

New data on the morphology of Sphenothallus Hall: implications for its affinities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73676/1/j.1502-3931.1992.tb01378.x.pd

Tree model guided candidate generation for mining frequent subtrees from XML

Due to the inherent flexibilities in both structure and semantics, XML association rules mining faces few challenges, such as: a more complicated hierarchical data structure and ordered data context. Mining frequent patterns from XML documents can be recast as mining frequent tree structures from a database of XML documents. In this study, we model a database of XML documents as a database of rooted labeled ordered subtrees. In particular, we are mainly coneerned with mining frequent induced and embedded ordered subtrees. Our main contributions arc as follows. We describe our unique embedding list representation of the tree structure, which enables efficient implementation ofour Tree Model Guided (TMG) candidate generation. TMG is an optimal, non-redundant enumeration strategy which enumerates all the valid candidates that conform to the structural aspects of the data. We show through a mathematical model and experiments that TMG has better complexity compared to the commonly used join approach. In this paper, we propose two algorithms, MB3Miner and iMB3-Miner. MB3-Miner mines embedded subtrees. iMB3-Miner mines induced and/or embedded subtrees by using the maximum level of embedding constraint. Our experiments with both synthetic and real datasets against two well known algorithms for mining induced and embedded subtrees, demonstrate the effeetiveness and the efficiency of the proposed techniques

Functional morphology and systematic position of tabulatomorphs

Tabulatomorph functional morphology being a reliable guide to locate the group among Metazoa, the authors, who were supplied with an abundant North-African material, offer evidence particularly to compare them with sponges. They provisionally conclude that most of them were allied to primitive sponges and even algae but achieved various differentiations more advanced than any of those