Approximation Algorithms for the Minimum-Length Corridor and Related Problems

On the Minimum Corridor Connection Problem and Other Generalized Geometric Problems

In this paper we discuss the complexity and approximability of the minimum corridor connection problem where, given a rectilinear decomposition of a rectilinear polygon into “rooms”, one has to find the minimum length tree along the edges of the decomposition such that every room is incident to a vertex of the tree. We show that the problem is strongly NP-hard and give a subexponential time exa...

New Heuristic Algorithms for Solving Single-Vehicle and Multi-Vehicle Generalized Traveling Salesman Problems (GTSP)

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

On the minimum corridor connection problem and other generalized geometric problems ⋆ ( Online

In this paper we discuss the complexity and approximability of the minimum corridor connection problem where, given a rectilinear decomposition of a rectilinear polygon into “rooms”, one has to find the minimum length tree along the edges of the decomposition such that every room is incident to a vertex of the tree. We show that the problem is strongly NP-hard and give an subexponential time ex...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Complexity of minimum corridor guarding problems

In this paper, the complexity of minimum corridor guarding problems is discussed. These problem can be described as: given a connected orthogonal arrangement of vertical and horizontal line segments and a guard with unlimited visibility along a line segment, find a tree or a closed tour with minimum total length along edges of the arrangement, such that if the guard runs on the tree or on the c...