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- Erik D. Demaine, Shay Mozes, Benjamin Rossman, Oren Weimann
- ACM Trans. Algorithms
- 2007

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)

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> · α<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)

- Erik D. Demaine, Gad M. Landau, Oren Weimann
- Algorithmica
- 2009

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)

- Philip N. Klein, Shay Mozes, Oren Weimann
- SODA
- 2009

We give an <i>O</i>(<i>n</i> log<sup>2</sup> <i>n</i>)-time, linear-space algorithm that, given a directed planar graph with positive and negative arc-lengths, and given a node <i>s</i>, finds the distances from <i>s</i> to all nodes.

- Amir Abboud, Virginia Vassilevska Williams, Oren Weimann
- ICALP
- 2014

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)

- Philip Bille, Gad M. Landau, Rajeev Raman, Kunihiko Sadakane, S. Srinivasa Rao, Oren Weimann
- SIAM J. Comput.
- 2015

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 Re-Pair. In… (More)

- Philip Bille, Inge Li Gørtz, Gad M. Landau, Oren Weimann
- Inf. Comput.
- 2013

Abstract. 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… (More)

Permutations on strings representing gene clusters on genomes have been studied earlier in [20, 15, 3, 13, 19] and the idea of a maximal permutation pattern was introduced in [13]. In this paper, we present a new tool for representation and detection of gene clusters in multiple genomes, using PQ trees [6]: this describes the inner structure and the… (More)

- Shay Mozes, Oren Weimann, Michal Ziv-Ukelson
- Algorithmica
- 2007

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)

- Shay Mozes, Krzysztof Onak, Oren Weimann
- SODA
- 2008

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)