How to Walk Your Dog in the Mountains with No Magic Leash

We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a $O(\log n)$-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic \Frechet distance, or the minimum height of a homotopy, is in NP

Bulletin of the Center for Children's Books 22 (11) 1969

published or submitted for publicatio

Animal Stories for Good Reference Librarians

This essay uses animals and animal-related metaphors to illustrate several short lessons about practicing reference

On the complexity of optimal homotopies

In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves $\gamma_1$ and $\gamma_2$ on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between $\gamma_1$ and $\gamma_2$ where the length of the longest intermediate curve is minimized. Such optimal homotopies are relevant for a wide range of purposes, from very theoretical questions in quantitative homotopy theory to more practical applications such as similarity measures on meshes and graph searching problems. We prove that Homotopy Height is in the complexity class NP, and the corresponding exponential algorithm is the best one known for this problem. This result builds on a structural theorem on monotonicity of optimal homotopies, which is proved in a companion paper. Then we show that this problem encompasses the Homotopic Fr\'echet distance problem which we therefore also establish to be in NP, answering a question which has previously been considered in several different settings. We also provide an O(log n)-approximation algorithm for Homotopy Height on surfaces by adapting an earlier algorithm of Har-Peled, Nayyeri, Salvatipour and Sidiropoulos in the planar setting

The Vehicle, Fall 2009

Table of Contents Poetry AliveRashelle McNairpage 3 Train of ThoughtsJeanette Saribekianpage 4 Biding the TideMarlee Lutzpage 5 Rotten HarvestJessyca Revillapage 15 Nostalgia ODJustine Fittonpage 16 Beyond WordsAshley Wrightpage 26 Don\u27tMelinda Knightpage 27 Happy HourStephen Garciapage 35 UntitledDaniel Paquinpage 37 Vibrant SensationsAshton Tembypage 38 Scarecrow Sally on a Saturday NightDaniel Davispage 45 The FarmAshley Wrightpage 49 Anything ButJustine Fittonpage 51 CrashDanielle Shirtinopage 53 Weathering SatisfactionRashelle McNairpage 54 SeminarDaniel Davispage 71 Nature\u27s Mood SwingsJeanette Saribekianpage 72 The PerformanceMelinda Knightpage 68 AmaterasuMarlee Lutzpage 82 Prose AirLauren Davidsonpage 6 The Twang of OrangesJ.T. Dawsonpage 18 ListenStephani Pescitellipage 29 The Rise and Fall of NickNickolas Alexanderpage 30 LossSimyona Deanovapage 39 Like DiamondsMark Rheaumepage 42 Moral FixationBryan Rolfsenpage 47 Reflections in College AlgebraNicole Reichertpage 52 LeashDaniel Paquinpage 56 I Lost My KeysJustine Fittonpage 75 A Third Grade EssayMark Rheaumepage 69 Be Careful, They BiteDaniel Davispage 84 Art Limb BurgAlycia Rockeycover AvesSamantha Flowerspage 14 Life-LuminescenceStephani Pescitellipage 25 MonopolyMegan Mathypage 28 Carousel NostalgiaAlycia Rockeypage 36 ShoesSarah Olsonpage 41 Waimea BayJarrod Taylorpage 50 Peacock Plumage Alycia Rockeypage 55 Building a HouseStephani Pescitellipage 70 ShellMegan Mathypage 74 From the VacationSamantha Flowerspage 73 Chicago CanopyAlycia Rockeypage 83 Features Editor\u27s NoteLindsey Durbinpage 1 LazarusDr. David Radavichpage 2 James K. Johnson Creative Writing Awardpage 88 Winning Entries (Poetry)Matthew J. Schumakepage 89 Winning Entry (Nonfiction)Jennifer O\u27Neilpage 92 Interview, 2009 Chapbook WinnerDaniel Davispage 95 Contributorspage 99https://thekeep.eiu.edu/vehicle/1090/thumbnail.jp