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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 give an O(n log3 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 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 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 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)
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)