Enumerating solutions to $p(a)+q(b)=r(c)+s(d)$

Enumerating All Solutions for Constraint Satisfaction Problems

We contribute to the study of efficient enumeration algorithms for all solutions of constraint satisfaction problems. The only algorithm known so far, presented by Creignou and Hébrard [CH97] and generalized by Cohen [Coh04], reduces the enumeration problem for a constraint language Γ to the decision problem for a slightly enlarged constraint language Γ, i.e., it yields an efficient enumeration...

On enumerating all minimal solutions of feedback problems

We present an algorithm that generates all (inclusion-wise) minimal feedback vertex sets of a directed graph G = (V, E). The feedback vertex sets of G are generated with a polynomial delay of O ( |V |(|V | + |E|) ) . We further show that the underlying technique can be tailored to generate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polyn...

Sign Methods for Enumerating Solutions of Nonlinear Algebraic Systems

We implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the algebraic signs of the components of the function. The basic theorems of Kronecker–Picard theory relate the number of roots to the topological degree. They are combined with grid methods in order to compute the topologic...

Counting the Solutions of Presburger Equations without Enumerating Them

Enumerating 3D-Sudoku Solutions over Cubic Prefractal Objects

We consider three-dimensional extensions of the Sudoku puzzle over prefractal objects. The prefractal objects we use are 2nd-level cubic approximations of two 3D fractals. Both objects are composed of 81 cubic pieces and they have 9× 9-grid appearances in three orthogonal directions. On each object, our problem is to assign a digit to each of the 81 pieces so that it has a Sudoku solution patte...