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The <i>edit distance</i> between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this article, we present a worst-case <i>O</i>(<i>n</i><sup>3</sup>)-time algorithm for the(More)
We introduce a new compression scheme for labeled trees based on top trees [3]. Our compression scheme is the first to simultaneously take advantage of internal repeats in the tree (as opposed to the classical DAG compression that only exploits rooted subtree repeats) while also supporting fast navigational queries directly on the compressed representation.(More)
We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree for the bottleneck edge query problem on trees and undirected graphs, and a proof that no Cartesian tree exists for the two-dimensional(More)
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures (sometimes with slight reduction in efficiency) many of the popular compression schemes, including the Lempel-Ziv family, Run-Length Encoding, Byte-Pair Encoding, Sequitur, and RePair. In this(More)
Let <i>S</i> be a string of length <i>N</i> compressed into a context-free grammar <i>S</i> of size <i>n</i>. We present two representations of <i>S</i> achieving <i>O</i>(log <i>N</i>) random access time, and either <i>O</i>(<i>n</i> &#183; &alpha;<sub><i>k</i></sub>(<i>n</i>)) construction time and space on the pointer machine model, or <i>O</i>(<i>n</i>)(More)
The Local Alignment problem is a classical problem with applications in biology. Given two input strings and a scoring function on pairs of letters, one is asked to find the substrings of the two input strings that are most similar under the scoring function. The best algorithms for Local Alignment run in time that is roughly quadratic in the string length.(More)
We present a method to speed up the dynamic program algorithms used for solving the HMM decoding and training problems for discrete time-independent HMMs. We discuss the application of our method to Viterbi’s decoding and training algorithms (IEEE Trans. Inform. Theory IT-13:260–269, 1967), as well as to the forward-backward and Baum-Welch (Inequalities(More)
We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor’s prices). The first player chooses an assignment of prices to the(More)
We address the extension of the binary search technique from sorted arrays and totally ordered sets to trees and tree-like partially ordered sets. As in the sorted array case, the goal is to minimize the number of queries required to find a target element in the worst case. However, while the optimal strategy for searching an array is straightforward(More)
When designing a preemptive online algorithm for the maximum matching problem, we wish to maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its(More)