Related papers: Solving Tantrix via Integer Programming
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…
The Number Rotation Puzzle (NRP) is a combination puzzle in which the goal is to rearrange a scrambled rectangular grid of numbers back into order via moves that consist of rotating square blocks of numbers of fixed size. Over all possible…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…
This paper presents an algorithm for computing the contraction of two-dimensional tensor networks on a square lattice; and we combine it with solving congruence equations to compute the exact enumeration (including weighted enumeration) of…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…
In areas as diverse as contemporary art, play structures, climbing equipment, and modular construction toys, we see the presence of building block-like polyhedral complexes, which are generalizations of the pieces in the game Tetris. We…
A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…
For robots to successfully execute tasks assigned to them, they must be capable of planning the right sequence of actions. These actions must be both optimal with respect to a specified objective and satisfy whatever constraints exist in…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
Holzer and Holzer (Discrete Applied Mathematics 144(3):345--358, 2004) proved that the Tantrix(TM) rotation puzzle problem with four colors is NP-complete, and they showed that the infinite variant of this problem is undecidable. In this…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…