Approximation algorithms for shortest descending paths in terrains

Authors:
Mustaq Ahmed;Sandip Das;Sachin Lodha;Anna Lubiw;Anil Maheshwari;Sasanka Roy
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;Indian Statistical Institute, Kolkata, India;Tata Consultancy Services Ltd., Pune, India;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada;Tata Consultancy Services Ltd., Pune, India
Venue:
Journal of Discrete Algorithms
Year:
2010

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Abstract

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a polyhedral terrain. We present two approximation algorithms that solve the SDP problem on general terrains. We also introduce a generalization of the shortest descending path problem, called the shortest gently descending path (SGDP) problem, where a path descends, but not too steeply. The additional constraint to disallow a very steep descent makes the paths more realistic in practice. We present two approximation algorithms to solve the SGDP problem on general terrains. All of our algorithms are simple, robust and easy to implement.