Edit distance

About: Edit distance is a research topic. Over the lifetime, 2887 publications have been published within this topic receiving 71491 citations.

Fuzzy Contour Trees: Alignment and Joint Layout of Multiple Contour Trees

Abstract: Author(s): Lohfink, AP; Wetzels, F; Lukasczyk, J; Weber, GH; Garth, C | Abstract: We describe a novel technique for the simultaneous visualization of multiple scalar fields, e.g. representing the members of an ensemble, based on their contour trees. Using tree alignments, a graph-theoretic concept similar to edit distance mappings, we identify commonalities across multiple contour trees and leverage these to obtain a layout that can represent all trees simultaneously in an easy-to-interpret, minimally-cluttered manner. We describe a heuristic algorithm to compute tree alignments for a given similarity metric, and give an algorithm to compute a joint layout of the resulting aligned contour trees. We apply our approach to the visualization of scalar field ensembles, discuss basic visualization and interaction possibilities, and demonstrate results on several analytic and real-world examples.

Tree edit distance cannot be computed in strongly subcubic time (unless APSP can)

Abstract: The edit distance between two rooted ordered trees with n nodes labeled from an alphabet Σ 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. Tree edit distance is a well known generalization of string edit distance. The fastest known algorithm for tree edit distance runs in cubic O(n3) time and is based on a similar dynamic programming solution as string edit distance. In this paper we show that a truly subcubic O(n3−ϵ) time algorithm for tree edit distance is unlikely: For |Σ| = Ω(n), a truly subcubic algorithm for tree edit distance implies a truly subcubic algorithm for the all pairs shortest paths problem. For |Σ| = O(1), a truly subcubic algorithm for tree edit distance implies an O(nk−ϵ) algorithm for finding a maximum weight k-clique. Thus, while in terms of upper bounds string edit distance and tree edit distance are highly related, in terms of lower bounds string edit distance exhibits the hardness of the strong exponential time hypothesis [Backurs, Indyk STOC'15] whereas tree edit distance exhibits the hardness of all pairs shortest paths. Our result provides a matching conditional lower bound for one of the last remaining classic dynamic programming problems.

A fast parallel algorithm to determine edit distance

Abstract: We consider the problem of determining in parallel the cost of converting a source string to a destination string by a sequence of insert, delete and transform operations. Each operation has an integer cost in some fixed range. We present an algorithm that runs in <9(logmlogrt) time and uses mn processors on a CRCW PRAM, where m and n are the lengths of the strings. The best known sequential algorithm [MP83] runs in time 0(n/ log n) for strings of length n, indicating that our parallel algorithm (with time-processor product equal to 0(mn log m log n)) is nearly optimal. An instance of the edit distance problem is represented as a graph. The algorithm finds the shortest path in the graph using a path doubling method with efficient pruning due to the structure of the problem. Extensions of the algorithm solve approximate string matching and local best fit problems. The problem of finding the largest common submatrix of two matrices is considered and shown to be NP-hard. Finally we present an algorithm for exact two-dimensional pattern matching that runs in OClog n) time using n processors for a n x n search matrix.

Error tolerant autocompletion

Abstract: Techniques for error-tolerant autocompletion are described. While displaying characters of an input string as they are inputted by a user, when a character is added to the input string by the user, matching strings may be selected from among a set of candidate strings by determining which of the candidate strings have a prefix whose characters match the characters of the input string within a given edit distance of the input string.

Sketching Earth-Mover Distance on Graph Metrics

Abstract: We develop linear sketches for estimating the Earth-Mover distance between two point sets, i.e., the cost of the minimum weight matching between the points according to some metric. While Euclidean distance and Edit distance are natural measures for vectors and strings respectively, Earth-Mover distance is a well-studied measure that is natural in the context of visual or metric data. Our work considers the case where the points are located at the nodes of an implicit graph and define the distance between two points as the length of the shortest path between these points. We first improve and simplify an existing result by Brody et al. [4] for the case where the graph is a cycle. We then generalize our results to arbitrary graph metrics. Our approach is to recast the problem of estimating Earth-Mover distance in terms of an l1 regression problem. The resulting linear sketches also yield space-efficient data stream algorithms in the usual way.