N2-o-Tolylbenzamidine

TAL Recognition in O(M(n2)) Time

We propose an O(M(n2)) time algorithm for the recognition of Tree Adjoining Languages (TALs), where n is the size of the input string and M(k) is the time needed to multiply two k x k boolean matrices. Tree Adjoining Grammars (TAGs) are formalisms suitable for natural language processing and have received enormous attention in the past among not only natural language processing researchers but ...

An O(n2) algorithm for signed translocation

Genome rearrangement is an important area in computational biology. There are three basic operations, reversal, translocation and transposition. Here we study the translocation operations. Multi-chromosomal genomes frequently evolve by translocation events that exchange genetic material between two chromosomes. We focus on the signed case, where the direction of each gene is known. The signed t...

On a Class of O(n2) Problems in Computational Geometry

There are many problems in computational geometry for which the best know algorithms take time 19(n 2) (or more) in the worst case while only very low lower bounds are known. In this paper we describe a large class of problems for which we prove that they are all at least as difficult as the following base problem 3SUM: Given a set S of n integers, are there three elements of S that sum up to 0...

Finding an o(n2 log n) Algorithm Is Sometimes Hard

Embedding into the rectilinear plane in optimal O(n2) time

In this paper, we present an optimal O(n) time algorithm for deciding if a metric space (X, d) on n points can be isometrically embedded into the plane endowed with the l1-metric. It improves the O(n 2 log n) time algorithm of J. Edmonds (2008). Together with some ingredients introduced by Edmonds, our algorithm uses the concept of tight span and the injectivity of the l1-plane. A different O(n...