Planning Monotone Paths to Visit a Set of Obstacles

1990 ◽  
Author(s):  
Laxmi P. Gewali
Keyword(s):  
Monotone Paths

scholarly journals Simple and optimal output-sensitive construction of contour trees using monotone paths

2005 ◽  
Vol 30 (2) ◽  
pp. 165-195 ◽  
Author(s):  
Yi-Jen Chiang ◽  
Tobias Lenz ◽  
Xiang Lu ◽  
Günter Rote
Keyword(s):  
Contour Trees ◽  
Optimal Output ◽  
Monotone Paths

Monotone Descent Path Queries on Dynamic Terrains

2014 ◽  
Vol 14 (1) ◽  
Author(s):  
Xiangzhi Wei ◽  
Ajay Joneja ◽  
Yaobin Tian ◽  
Yan-An Yao
Keyword(s):  
Data Structure ◽  
Engineering Design ◽  
Linear Time ◽  
Monotone Path ◽  
Path Queries ◽  
Contour Tree ◽  
Monotone Paths

Monotone paths are useful in many engineering design applications. In this paper, we address the problem of answering monotone descent path queries on terrains that are continually changing. A terrain can be represented by a unique contour tree. Such a contour tree belongs to a class of graphs called arbitrarily directed trees (ADTs). Let T be an ADT with n nodes. In this paper, we present a new linear time preprocessing algorithm for decomposing a static ADT T into a forest F, with which we can answer lowest common descendent (LCA) queries in O(1) time. This is useful in answering monotone path queries on the corresponding terrain. We show how to maintain this data structure, and thereby answer LCA queries efficiently, for dynamic ADTs. We also show how to maintain the data structure of dynamic terrains, while simultaneously maintaining the corresponding contour tree. This allows us to efficiently answer monotone path queries between any two points on dynamic terrains.

scholarly journals On the Length of Monotone Paths in Polyhedra

2021 ◽  
Vol 35 (3) ◽  
pp. 1746-1768
Author(s):  
Moïse Blanchard ◽  
Jesús A. De Loera ◽  
Quentin Louveaux
Keyword(s):  
Monotone Paths

scholarly journals Ramsey numbers for degree monotone paths

2017 ◽  
Vol 340 (2) ◽  
pp. 124-131
Author(s):  
Yair Caro ◽  
Raphael Yuster ◽  
Christina Zarb
Keyword(s):  
Ramsey Numbers ◽  
Monotone Paths

scholarly journals Monotone paths in line arrangements

2003 ◽  
Vol 24 (3) ◽  
pp. 129-134 ◽  
Author(s):  
Radoš Radoičić ◽  
Géza Tóth
Keyword(s):  
Line Arrangements ◽  
Monotone Paths

scholarly journals Monotone Paths in Geometric Triangulations

2018 ◽  
Vol 62 (6) ◽  
pp. 1490-1524
Author(s):  
Adrian Dumitrescu ◽  
Ritankar Mandal ◽  
Csaba D. Tóth
Keyword(s):  
Monotone Paths

scholarly journals Nearly-linear monotone paths in edge-ordered graphs

2020 ◽  
Vol 238 (2) ◽  
pp. 663-685
Author(s):  
Matija Bucić ◽  
Matthew Kwan ◽  
Alexey Pokrovskiy ◽  
Benny Sudakov ◽  
Tuan Tran ◽  
...  
Keyword(s):  
Ordered Graphs ◽  
Monotone Paths

scholarly journals Finding monotone paths in edge-ordered graphs

2010 ◽  
Vol 158 (15) ◽  
pp. 1624-1632 ◽  
Author(s):  
J. Katrenič ◽  
G. Semanišin
Keyword(s):  
Ordered Graphs ◽  
Monotone Paths
Sign in / Sign up

Export Citation Format

Share Document