We first draw a Cartesian coordinate mesh on the two dimensional Euclidean plane so that each intersection point has integer coordinates. We call these intersection points lattice points. We want to label lattice points in an orderly fashion so that each label is determined by two of its neighboring labels. We proceed with the following rule. If the label given to a lattice point with coordinat...

The hop constrained min-sum arborescence with outage costs problem consists of selecting links in a network so as to connect a set of terminal nodes N={2,3,......n} to a central node with minimal total link cost such that (a) each terminal node j has exactly one entering link; (b) for each terminal node j, a unique path from the central node to j exists; (c) for each terminal node j the number ...

In this last of three papers on simplicial tree-decompositions of graphs we investigate the extent to which prime factors in such decompositions are unique, or depend on the decomposition chosen. A simple example shows that a prime decomposition of a graph may have superfluous factors, the omission of which leaves a set of factors that can be rearranged into another decomposition of the same gr...

Abstract—In the restructured electricity markets, the generators and the Independent System Operator (ISO) play important roles in the balance of electricity supply and demand. We consider a mixed integer bi-level model reformulated as a mathematical program with complementary constraints (MPCC) in which a single conceptual leader decides the transmission line expansion plan and generators plan...

Gomory-Chvátal cuts are prominent in integer programming. The Gomory-Chvátal closure of a polyhedron is the intersection of all half spaces defined by its Gomory-Chvátal cuts. In this paper, we show that it is NP-complete to decide whether the Gomory-Chvátal closure of a rational polyhedron is empty, even when this polyhedron contains no integer point. This implies that the problem of deciding ...

Chvátal-Gomory and Gomory fractional cuts are well-known cutting planes for pure integer programming problems. Various methods for strengthening them are known, for example based on subadditive functions or disjunctive techniques. We present a new and surprisingly simple strengthening procedure, discuss its properties, and present some computational results.

We survey some of the recent results on the complexity of recognizing n{dimensional linear arrangements and convex polyhedra by randomized algebraic decision trees. We give also a number of concrete applications of these results. In particular, we derive rst nontrivial, in fact quadratic, randomized lower bounds on the problems like Knapsack and Bounded Integer Programming. We formulate further...

We present a data structure to index a specific kind of factors, that is of substrings, called gapped-factors. A gapped-factor is a factor containing a gap that is ignored during the indexation. The data structure presented is based on the suffix tree and indexes all the gapped-factors of a text with a fixed size of gap, and only those. The construction of this data structure is done online in ...

Two-group classification is a key task in decision making and data mining applications. We introduce two new mixed integer programming formulations that make use of multiple separating hyperplanes. They represent a generalization of previous piecewise-linear models that embed rules having the form of hyperplanes, which are used to successively separate the two groups. In fact, the classifiers o...

One typically proves infeasibility in satisfiability/constraint satisfaction (or optimality in integer programming) by constructing a tree certificate. However, deciding how to branch in the search tree is hard, and impacts search time drastically. We explore the power of a simple paradigm, that of throwing random darts into the assignment space and then using information gathered by that dart ...