The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In this paper we generalize the LCE problem to trees and suggest a few applications of LCE in trees to tries and XML databases. Given a labeled and ...

We present an approximation algorithm that, given a simple, possibly nonconvex polyhedron P with n vertices in R 3 , and two points s and t on its surface @P , constructs a path on @P between s and t whose length is at most 7(1 + "), where is the length of the shortest path between s and t on @P , and " > 0 is an arbitararily small positive constant. The algorithm runs in O(n 5=3 log 5=3 n) tim...

Given a dynamic network with n nodes and m arcs in which all attributes including travel times, travel costs and waiting costs may change dynamically over a time horizon T. The dynamic shortest path problem is to determine a path from a specified source node to every other node with minimal total cost, subject to the constraint that the total traverse time is at most T. This problem can be form...

Given a directed graph G and a parameter k, the Long Directed Cycle (LDC) problem asks whether G contains a simple cycle on at least k vertices, while the k-Path problems asks whether G contains a simple path on exactly k vertices. Given a deterministic (randomized) algorithm for k-Path as a black box, which runs in time t(G, k), we prove that LDC can be solved in deterministic time O(max{t(G, ...

Given an undirected graph G and vertices s, t ∈ V (G), the undirected connectivity problem is to decide whether there is a path from s to t in G. If G has N vertices and M edges, then the existence of a path between s and t implies the existence of a path of length at most N . If A is the adjacency matrix of G and G has, without loss of generality, self-loops on every vertex, then s and t are c...

A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e. a hamiltonian path. Given a tournament T , it is well known that it contains a directed hamiltonian path. In this paper, we develop the structure necessary for a tournament T to contain an arc xy that is not on any hamiltonian path. Using this structure, we give suff...

Let s be a source point and t be a destination point inside an n-vertex simple polygon P . Euclidean shortest paths [Lee and Preparata, Networks, 1984; Guibas et al. , Algorithmica, 1987] and minimum-link paths [Suri, CVGIP, 1986; Ghosh, J. Algorithms, 1991] between s and t inside P have been well studied. Both these kinds of paths are simple and piecewise-convex. However, computing optimal pat...

ONE-DIMENSIONAL EDWARDS MODEL Mar h 6, 2002 Rem o van der Hofstad 1 2 Frank den Hollander 3 Wolfgang K onig 4 Abstra t: In this paper we prove a large deviation prin iple for the empiri al drift of a onedimensional Brownian motion with self-repellen e alled the Edwards model. Our results extend earlier work in whi h a law of large numbers, respe tively, a entral limit theorem were derived. In ...

a r t i c l e i n f o a b s t r a c t Path testing is the strongest coverage criterion in white box testing. Finding target paths is a key challenge in path testing. Genetic algorithms have been successfully used in many software testing activities such as generating test data, selecting test cases and test cases prioritization. In this paper, we introduce a new genetic algorithm for generating...

We study a quantum system in a Riemannian manifoldM on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q = M/G and the reduced path integrals are completely classified by irreducible unitary representations of G. It is not necessary to assume that the action of G on M is either free or transitive. Hence the quotien...