Single-face non-crossing shortest paths in planar graphs
Steiger, Alexander John
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https://hdl.handle.net/2142/98345
Description
Title
Single-face non-crossing shortest paths in planar graphs
Author(s)
Steiger, Alexander John
Issue Date
2017-07-13
Director of Research (if dissertation) or Advisor (if thesis)
Erickson, Jeff
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Planar graphs
Non-crossing paths
Shortest paths
Abstract
We consider the following problem: Given an n-vertex undirected planar-embedded graph with a simple boundary cycle, non-negative edge lengths, and k pairs of terminals {(s_1,t_1),(s_2,t_2),...,(s_k,t_k)} specified on the boundary, find non-crossing shortest paths connecting all pairs of terminals (if any such paths exist). We present an algorithm to find such paths in O(n log log k) time which improves upon the previous best runtime of O(n log k) by Takahashi, Suzuki, and Nishizeki [Algorithmica 1996].
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