Chapter

WALCOM: Algorithms and Computation

Volume 5431 of the series Lecture Notes in Computer Science pp 59-70

Shortest Gently Descending Paths

  • Mustaq AhmedAffiliated withD. R. C. School of Computer Science, University of Waterloo
  • , Anna LubiwAffiliated withD. R. C. School of Computer Science, University of Waterloo
  • , Anil MaheshwariAffiliated withSchool of Computer Science, Carleton University

* Final gross prices may vary according to local VAT.

Get Access

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. We 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 give two approximation algorithms (more precisely, FPTASs) to solve the SGDP problem on general terrains.