In this paper, we will introduce an exact algorithm with a time complexity of O(1.299) for the weighted mutually exclusive set cover problem, where m is the number of subsets in the problem. This problem has important applications in recognizing mutation genes that cause different cancer diseases.

We describe a new algorithm for computing a Nash equilibrium in graphical games, a compact representation for multi-agent systems that we introduced in previous work. The algorithm is the first to compute equilibria both efficiently and exactly for a non-trivial class of graphical games.

In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes distortion (the DISTORTION problem). For both problems we develop algorithms that work in O(9.363) time and polynomial space. For BANDWIDTH, this improves O(10...

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 ...