String graphs requiring exponential representations
Journal of Combinatorial Theory Series B
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
k-Pairs Non-Crossing Shortest Paths in a Simple Polygon
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Algorithms for Finding Non-Crossing Paths with Minimum Total Length in Plane Graphs
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Finding Shortest Non-Crossing Rectilinear Paths in Plane Regions
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Journal of Computer and System Sciences - STOC 2001
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Thick non-crossing paths and minimum-cost flows in polygonal domains
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Thick non-crossing paths and minimum-cost continuous flows in polygonal domains
Thick non-crossing paths and minimum-cost continuous flows in polygonal domains
Computing homotopic shortest paths efficiently
Computational Geometry: Theory and Applications
Spiraling and Folding: The Word View
Algorithmica - Special issue: Algorithms, Combinatorics, & Geometry
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Let G be an n-vertex plane graph with non-negative edge weights, and let k terminal pairs be specified on h face boundaries. We present an algorithm to find k non-crossing walks in G of minimum total length that connect all terminal pairs, if any such walks exist, in 2O(h2)n log k time. The computed walks may overlap but may not cross each other or themselves. Our algorithm generalizes a result of Takahashi, Suzuki, and Nishizeki [Algorithmica 1996] for the special case h ≤ 2. We also describe an algorithm for the corresponding geometric problem, where the terminal points lie on the boundary of h polygonal obstacles of total complexity n, again in 2O(h2)n time, generalizing an algorithm of Papadopoulou [Int. J. Comput. Geom. Appl. 1999] for the special case h ≤ 2. In both settings, shortest non-crossing walks can have complexity exponential in h. We also describe algorithms to determine in O(n) time whether the terminal pairs can be connected by any non-crossing walks.