Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A better heuristic for orthogonal graph drawings
Computational Geometry: Theory and Applications
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
TSP with neighborhoods of varying size
Journal of Algorithms
Complexity of the minimum-length corridor problem
Computational Geometry: Theory and Applications
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Planar Branch Decompositions II: The Cycle Method
INFORMS Journal on Computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
New upper bounds on the decomposability of planar graphs
Journal of Graph Theory
Optimal branch-decomposition of planar graphs in O(n3) time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximation algorithms for euclidean group TSP
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On the minimum corridor connection problem and other generalized geometric problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Connecting face hitting sets in planar graphs
Information Processing Letters
Complexity of minimum corridor guarding problems
Information Processing Letters
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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 exact algorithm. For the special case when the room connectivity graph is k-outerplanar the algorithm running time becomes cubic. We develop a polynomial time approximation scheme for the case when all rooms are fat and have nearly the same size. When rooms are fat but are of varying size we give a polynomial time constant factor approximation algorithm.