Beyond Steiner's problem: a VLSI oriented generalization
WG '89 Proceedings of the fifteenth international workshop on Graph-theoretic concepts in computer science
Bounds on the quality of approximate solutions to the group Steiner problem
WG '90 Proceedings of the 16th international workshop on Graph-theoretic concepts in computer science
Provably good routing tree construction with multi-port terminals
Proceedings of the 1997 international symposium on Physical design
Approximation algorithms for set cover and related problems
Approximation algorithms for set cover and related problems
On the complexity of approximating tsp with neighborhoods and related problems
Computational Complexity
Complexity of the minimum-length corridor problem
Computational Geometry: Theory and Applications
On trip planning queries in spatial databases
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
On the minimum corridor connection problem and other generalized geometric problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Complexity of minimum corridor guarding problems
Information Processing Letters
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Given a rectangular boundary partitioned into rectangles, the Minimum-Length Corridor (MLC-R) problem consists of finding a corridor of least total length. A corridor is a set of connected line segments, each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectangles, and must include at least one point from the boundary of every rectangle and from the rectangular boundary. The MLC-R problem is known to be NP-hard. We present the first polynomial-time constant ratio approximation algorithm for the MLC-R and MLCk problems. The MLCk problem is a generalization of the MLC-R problem where the rectangles are rectilinear c-gons, for c ≤ k and k is a constant. We also present the first polynomial-time constant ratio approximation algorithm for the Group Traveling Salesperson Problem (GTSP) for a rectangular boundary partitioned into rectilinear c-gons as in the MLCk problem. Our algorithms are based on the restriction and relaxation approximation techniques.