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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)

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

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)

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)

- 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)

- 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)

- 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)

- Leah Epstein, Asaf Levin, Danny Segev, Oren Weimann
- STACS
- 2013

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)

We start a systematic study of data structures for the nearest colored node problem on trees. Given a tree with colored nodes and weighted edges, we want to answer queries (v, c) asking for the nearest node to node v that has color c. This is a natural generalization of the well-known nearest marked ancestor problem. We give an O(n)-space O(log log n)-query… (More)

- Shay Mozes, Cyril Nikolaev, Yahav Nussbaum, Oren Weimann
- ArXiv
- 2015

We give an O(n log log n) time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest

We give an O(n log 2 n)-time, linear-space algorithm that, given a directed planar graph with positive and negative arc-lengths, and given a node s, finds the distances from s to all nodes. The best previously known algorithm requires O(n log 3 n) time and O(n log n) space. 1 Introduction The problem of directed shortest paths with negative lengths is as… (More)