Python implementation of Algorithm X by Knuth is presented. Algorithm X finds all solutions to the exact cover problem. The exemplary results for pentominoes, Latin squares and Sudoku are given.

A hidden guard set G is a set of point guards in polygon P that all points of the polygon are visible from some guards in G under the constraint that no two guards may see each other. In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility. Two points p and q are orthogonally visible if the orthogonal bounding rectangle for ...

In this paper, we present an exact algorithm for the Steiner tree problem. The algorithm is based on certain pre-computed index structures. Our algorithm offers a practical solution for the Steiner tree problems on graphs of large size and bounded number of terminals.

Given a graph G = (V, E) with a length function on edges and a subset R of V , the full Steiner tree is defined to be a Steiner tree in G with all the vertices of R as its leaves. Then the full Steiner tree problem is to find a full Steiner tree in G with minimum length, and the bottleneck full Steiner tree problem is to find a full Steiner tree T in G such that the length of the largest edge i...

Weextend an hypergraph representation, introducedby Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming (Energy minimization, partition function, base-pair probabilities. . . ) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one t...

We present a continuous, bilinear formulation for the fixed charge network flow problem. This formulation is used to derive an exact algorithm for the fixed charge network flow problem converging in a finite number of steps. Some preliminary computational experiments are reported to show the performance of the algorithm.

In this article we first review previous integer formulations for the maximum diversity problem. This problem consists of selecting a subset of elements from a data set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and expressions for upper bounds for this problem. As far as we know, this is the first exact algorith...

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by other columns that correspond to irreducible solutions of certain linear diophantine inequalities. We prove that various versions of our algorithm are finite. It is a major conc...

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P1 and P2 such that the sum of the perimeters of ch(P1) and ch(P2) is minimized, where ch(Pi) denotes the convex hull of Pi. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n2) time algorithm. Despite considerable progress on related problems, no subquadratic time algo...

environmental pollution of subsurface due to the long time required to detect the onset of infection and spent considerable time and costs, has a special sensitivity. the aim of this research was, investigating the exact type and behavior of pollutants, assesses environmental attributes and measurement of some important factors of oil contamination in soils around the refinery and how the range...