Files in this item
Files | Description | Format |
---|---|---|
application/pdf ![]() | (no description provided) |
Description
Title: | The Fréchet distance revisited and extended |
Author(s): | Raichel, Benjamin A. |
Advisor(s): | Har-Peled, Sariel |
Department / Program: | Computer Science |
Discipline: | Computer Science |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | M.S. |
Genre: | Thesis |
Subject(s): | Frechet Distance
Approximation Algorithms Realistic Input Models |
Abstract: | Given two simplicial complexes, and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the Frechet distance between these curves is minimized. As a polygonal curve is a complex, this generalizes the regular notion of Frechet distance between curves. We also generalize the algorithm to handle an input of k simplicial complexes. Using this new algorithm we can solve a slew of new problems, from computing a median curve for a given collection of curves, to various motion planning problems. Additionally, we show that for the median curve problem, when the k input curves are c-packed, one can (1+epsilon)-approximate the median curve in near linear time, for fixed k and epsilon. |
Issue Date: | 2011-05-25 |
URI: | http://hdl.handle.net/2142/24109 |
Rights Information: |
Copyright 2011 Benjamin A. Raichel |
Date Available in IDEALS: | 2011-05-25 |
Date Deposited: | 2011-05 |
This item appears in the following Collection(s)
-
Dissertations and Theses - Computer Science
Dissertations and Theses from the Dept. of Computer Science -
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois