We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by obtaining the first polynomial time algorithms in several application areas including multicommodity flows and privacy in statistical databases.

The selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed-integer or integer linear program. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We present a new approach that relies on estimating the impact of the candidate variables on the active constr...

In this paper, we propose an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication. The proposed work will of great importance in applications which requires variable precision floating point multiplication such as multi-media processing applications. In the proposed architecture/methodology, we propose the replacement of exis...

In this short paper, a uniied framework for solving Boolean, integer and set constraints is presented. The computation model for solving conjunctions of primitive constraints, possibly with existential and universal quantiications, is described using rewrite rules. An important feature of the constraint solving model is that a variable's domain (set of integers) can be a constrained variable (s...

Do numbers play dice? In many ways, the answer seems to be yes. For example, whether an integer has an even or odd number of factors in its prime factorization is a property that behaves much like the outcome of a coin toss: The even/odd sequence obtained, say, from a stretch of one hundred consecutive integers, is, at least on the surface, indistinguishable from the heads/tails sequence obtain...

We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that reduce the variable domains. We compare these approaches using a set of benchmarks.

The Generalized Travelling Salesman Problem, denoted by GTSP, is a variant of the classical travelling salesman problem (TSP), in which the nodes of an undirected graph are partitioned into node sets (clusters) and the salesman has to visit exactly one node from every cluster. In this paper we described six distinct formulations of the GTSP as an integer programming. Apart from the standard for...

An Ordered Binary Decision Diagram (OBDD) is a directed acyclic graph representing a Boolean function. The size of OBDDs largely depends on the variable ordering. In this paper, we show the size of the OBDD representing the i-th bit of the output of n-bit/n-bit integer division is (2 (n?i)=8) for any variable ordering. We also show that _-OBDDs, ^-OBDDs and-OBDDs representing integer division h...

We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In [7], we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to solve the continuous relaxation problem. In t...

We study mixed integer nonlinear programs (MINLP)s that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is “turned off”, forces some of the decision variables to assume fixed values, and, when it is “turned on”, forces them to belong to a convex set. Many practical MINLPs contain integer ...