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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)

Given an n-vertex planar directed graph with real edge lengths and with no negative cycles, we show how to compute single-source shortest path distances in the graph in O(n log 2 n/ log log n) time with O(n) space. This is an improvement of a recent time bound of O(n log 2 n) by Klein et al.

We present new and improved data structures that answer exact node-to-node distance queries in planar graphs. Such data structures are also known as distance oracles. For any directed planar graph on n nodes with non-negative lengths we obtain the following: 1 • Given a desired space allocation S ∈ [n lg lg n, n 2 ], we show how to construct iñ O(S) time a… (More)

We give an O(n log 3 n) algorithm that, given an n-node directed planar graph with arc capacities, a set of source nodes, and a set of sink nodes, finds a maximum flow from the sources to the sinks. Previously, the fastest algorithms known for this problem were those for general graphs.

We describe a data structure for submatrix maximum queries in Monge matrices or Monge partial matrices, where a query specifies a contiguous submatrix of the given matrix , and its output is the maximum element of that subma-trix. Our data structure for an n × n Monge matrix takes O(n log n) space, O(n log 2 n) preprocessing time, and can answer queries in… (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)

We give an O(n 1.5 log n) algorithm that, given a directed planar graph with arc capacities, a set of source nodes and a single sink node, finds a maximum flow from the sources to the sink. This is the first subquadratic-time strongly polynomial algorithm for the problem.

- Philip N Klein, Shay Mozes
- 2009

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.

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)

Given a triangulated planar graph G on n vertices and an integer r<n, an <i>r--division</i> of G with <i>few holes</i> is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are not faces of G (also called <i>holes</i>), and such that, for each region, the total number of vertices… (More)