We consider the problem of augmenting a graph with n vertices embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present an exact algorithm for the cases when the input graph is a path that runs in O(n log n) time. We also present an algorithm that computes a (1 + ε)approximation in O(n+1/ε) time for paths in R, where d is a...

In the Intervalizing Colored Graphs problem, one must decide for a given graph G = (V,E) with a proper vertex coloring of G whether G is the subgraph of a properly colored interval graph. For the case that the number of colors k is xed, we give an exact algorithm that uses O∗(2n/log (n)) time for all > 0. We also give an O∗(2n) algorithm for the case that the number of colors k is not xed.

In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...

It is generally believed that the preference ranking method PROMETHEE has a quadratic time complexity. In this paper, however, we present an exact algorithm that computes PROMETHEE’s net flow scores in time O(qn log(n)), where q represents the number of criteria and n the number of alternatives. The method is based on first sorting the alternatives after which the unicriterion flow scores of al...

This paper presents an exact algorithm for the Lock Scheduling Problem (LSP) based on a Combinatorial Benders decomposition. LSP consists of three strongly interconnected sub problems: scheduling the lockages, assigning ships to chambers, and positioning the ships inside the chambers. These three sub problems are interpreted resp. as a scheduling, an assignment, and a packing problem. By combin...

this text carries out some ideas about exact and p− exact sequences of transformationsemigroups. some theorems like the short five lemma (lemma 1.3 and lemma 2.3) are valid here as inexact sequences of r − modules.