Several graphical structural models, including some models with latent variables can be viewed as models of conditional independence structure. However, usual graphical methods do not allow one to describe all possible stochastic conditional independence structures. Therefore an attempt to develop a general method of mathematical description of conditional independence structures by means of ce...

We study the use of binary variables in reformulating general mixed-integer linear programs. We show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching. We also give computational results on the performance of such reformulations in solving the mixed-integer programs, which support our...

Supported by NSF grant ECS-8418392 I n t r o d u c t i o n The Integer Programming (feasibility) Problem is the problem of determining whether there is a vector of integers satisfying a given system of linear inequalities. In settling an important open problem, H.W.Lenstra (1981,1983) showed in an elegant way that when n the number of variables is fixed, there is a polynomial t ime algorithm to...

We study the mixed–integer knapsack polyhedron, that is, the convex hull of the mixed–integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet–defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalit...

Process management simulation manages the execution of simulated processes. Each simulated process is comprised of a program that manipulates (sets/updates) the value of a single integer variable. Thus the state of a simulated process at any instant is comprised of the value of its integer variable and the value of its program counter. A simulated process’ program consists of a sequence of inst...

ABSTRACT A new method called variable reduction method for a classes of pure integer linear programming problems in single stage, is introduced which is better than the cutting plane method and the branch bound method. Both easy to understand and to apply, the variable reduction method can serve as an effective tool for solving integer linear programming problems while making the method accessi...

Pipeline are known as the most reliable and economical mode of transportation for petroleum and its derivatives, especially when large amounts of products have to be pumped for large distances. In this work we address the short-term schedule of a pipeline system comprising the distribution of several petroleum derivatives from a single oil refinery to several depots, connected to local consumer...

Given an invariant J(K) of a knot K, the corresponding (1, 1)-tangle invariant J ′(K) = J(K)/J(U) is defined as the quotient of J(K) by its value J(U) on the unknot U . We prove here that J ′ is always an integer 2-variable Laurent polynomial when J is the Homfly satellite invariant determined by decorating K with any eigenvector of the meridian map in the Homfly skein of the annulus. Specialis...

We study the characteristic function and moments of the integer-valued random variable bX+αc, whereX is a continuous random variable. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variable. This leads to oscillatory terms in asymptotics for these variables, something ...

NK landscapes (NKL) are stochastically generated pseudoboolean functions with N bits (genes) and K interactions between genes. By means of the parameter K ruggedness as well as the epistasis can be controlled. NKL are particularly useful to understand the dynamics of evolutionary search. We extend NKL from the traditional binary case to a mixed variable case with continuous, nominal discrete, a...