“Maximal-munch” tokenization in linear time

Edvard Munch Edvard Munch

Finding Maximal Repetitions in a Word in Linear Time

A repetition in a word is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in , that is those for which any extended subword of has a bigger period. The set of such repetitions represents in a compact way all repetitions in . We first prove a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of le...

Self-Stabilizing Maximal K-Dependent Sets In Linear Time

In a graph or network G = (V;E), a set S V is k-dependent if no node in S has more than k neighbors in S. We show that for each k 0 there is a self-stabilizing algorithm that identi es a maximal k-dependent set, and stabilizes in O(m + n) time. An interesting by-product of our paper is the new result that in any graph there exists a set that is both maximal k-dependent and minimal (k+1)-dominat...

A Linear Time Algorithm For Finding Maximal Planar Subgraphs

Given an undirected graph G, the maximal planar subgraph problem is to determine a planar subgraph H of G such that no edge of G-H can be added to H without destroying planarity. Polynomial algorithms have been obtained by Jakayumar, Thulasiraman and Swamy [6] and Wu [9]. O(mlogn) algorithms were previously given by Di Battista and Tamassia [3] and Cai, Han and Tarjan [2]. A recent O(m α α (n))...

A Linear Time Algorithm for the k Maximal Sums Problem

Finding the sub-vector with the largest sum in a sequence of n numbers is known as the maximum sum problem. Finding the k sub-vectors with the largest sums is a natural extension of this, and is known as the k maximal sums problem. In this paper we design an optimal O(n+k) time algorithm for the k maximal sums problem. We use this algorithm to obtain algorithms solving the two-dimensional k max...