One of the criteria for inferring a species tree from a collection of gene trees, when gene tree incongruence is assumed to be due to incomplete lineage sorting (ILS), is Minimize Deep Coalescence (MDC). Exact algorithms for inferring the species tree from rooted, binary trees under MDC were recently introduced. Nevertheless, in phylogenetic analyses of biological data sets, estimated gene tree...

This paper proposes a uniform framework for the development of parsing and translation algorithms for weighted extended (top-down) tree transducers and input strings. The asymptotic time complexity of these algorithms can be improved in practice by exploiting an algorithm for rule factorization in the above transducers.

This paper presents a simple method to build tree data structures which achieve just O(log N) visited nodes and O(D) compared digits (bits or bytes) per search or update, where N is the number of keys and D is the length of the keys, irrespectively of the order of the updates and of the digital representation of the keys. The additional space required by the method is asymptotically dismissable...

The tree inclusion problem is, given two node-labeled trees P and T (the “pattern tree” the “target tree”), to locate every minimal subtree in (if any) that can be obtained by applying a sequence of node insertion operations P. Although ordered is solvable polynomial time, unordered NP-hard. currently fastest algorithm for latter classic Kilpeläinen Mannila from 1995 runs O(d22dmn) where m n ar...

We improve the current complexities for maintaining a chordal graph by starting with an empty graph and repeatedly adding or deleting edges.

This chapter deals with the application of evolutionary approaches and other metaheuristic techniques for generating tree decompositions. Tree decomposition is a concept introduced by Robertson and Seymour [34] and it is used to characterize the difficulty of constraint satisfaction and NP-hard problems that can be represented as a graph. Although in general no polynomial algorithms have been f...

The Peano Count Tree (P-tree) is a quadrant-based lossless tree representation of the original spatial data. The idea of P-tree is to recursively divide the entire spatial data, such as Remotely Sensed Imagery data, into quadrants and record the count of 1-bits for each quadrant, thus forming a quadrant count tree. Using P-tree structure, all the count information can be calculated quickly. Thi...

Accurate modelling of individual trees is essential for forestry applications e.g. forestry inventory and biomass estimation. This paper aims to utilise Terrestrial Laser Scanners (TLS) in order to derive a three dimensional (3D) tree structure and compute its volume. A new approach is proposed and tested to estimate the tree structure and leaf area using precise voxel-based tree models. In thi...

Tree-Structured Vector Quantization (TSVQ) is a highly efficient technique for locating an appropriate codeword for each input vector. The algorithm does not guarantee that the selected codeword is the closest one to the input vector. Consequently, the image quality of TSVQ is worse than that of full-search VQ (FSVQ). Although researchers have proposed multipath TSVQ and DP-TSVQ to enhance the ...