The best known method for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically safe results, independent of the floating-point accuracy of linearprogramming software. Our work includes an improved branch-and-bound a...

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linearprogramming relaxation, loopy-belief propagation, and a leaf-removal algorithm. T...

We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon P with n vertices in a read only memory, and additional working memory of size m, the new algorithm computes the shortest path (in P ) in O(n2/m) expected time, assuming m = O(n/ log ...

With the increased sophistication of both computers and optimization software, linear programming problems of a size inconceivable to solve only a few years ago are now readily accessible. As model size and complexity increase, the issue of feasibility becomes a major issue in model development. This thesis explores the analysis of linear programming in-feasibility through the use of Irreducibl...

This paper describes a method to recommend allocation of generating units, with a view to achieve cost-effective control of particulate and gaseous emissions over tm energy scenario. Definition of relative cost and relative emission, with respect to corresponding base-case values, allows one to develop a model that describes cost and emission aspects of the chosen scenario. Optimisation of this...

The sign-rank of a real matrix M is the least rank of a matrix R in which every entry has the same sign as the corresponding entry of M.We determine the sign-rank of every matrix of the form M = [ D(|x ∧ y|) ]x,y, where D : {0, 1, . . . , n} → {−1,+1} is given and x and y range over {0, 1}n . Specifically, we prove that the sign-rank of M equals 22̃(k), where k is the number of times D changes s...