On finding widest empty curved corridors

Open archive-ElsevierAn α-siphon of width w is the locus of points in the plane that are at the same distance w from a 1-corner polygonal chain C such that α is the interior angle of C. Given a set P of n points in the plane and a fixed angle α, we want to compute the widest empty α-siphon that splits P into two non-empty sets.We present an efficient O(n log3 n)-time algorithm for computing the widest oriented α-siphon through P such that the orientation of a half-line of C is known.We also propose an O(n3 log2 n)-time algorithm for the widest arbitrarily-oriented version and an (nlog n)-time algorithm for the widest arbitrarily-oriented α-siphon anchored at a given point

Minimax and Maximin Fitting of Geometric Objects to Sets of Points

This thesis addresses several problems in the facility location sub-area of computational geometry. Let S be a set of n points in the plane. We derive algorithms for approximating S by a step function curve of size k \u3c n, i.e., by an x-monotone orthogonal polyline ℜ with k \u3c n horizontal segments. We use the vertical distance to measure the quality of the approximation, i.e., the maximum distance from a point in S to the horizontal segment directly above or below it. We consider two types of problems: min-ε, where the goal is to minimize the error for a given number of horizontal segments k and min-#, where the goal is to minimize the number of segments for a given allowed error ε. After O(n) preprocessing time, we solve instances of the latter in O(min{k log n, n}) time per instance. We can then solve the former problem in O(min{n2, nk log n}) time. Both algorithms require O(n) space. The second contribution is a heuristic for the min-ε problem that computes a solution within a factor of 3 of the optimal error for k segments, or with at most the same error as the k-optimal but using 2k - 1 segments. Furthermore, experiments on real data show even better results than what is guaranteed by the theoretical bounds. Both approximations run in O(n log n) time and O(n) space. Then, we present an exact algorithm for the weighted version of this problem that runs in O(n2) time and generalize the heuristic to handle weights at the expense of an additional log n factor. At this point, a randomized algorithm that runs in O(n log2 n) expected time for the unweighted version is presented. It easily generalizes to the weighted case, though at the expense of an additional log n factor. Finally, we treat the maximin problem and present an O(n3 log n) solution to the problem of finding the furthest separating line through a set of weighted points. We conclude with solutions to the obnoxious wedge problem: an O(n2 log n) algorithm for the general case of a wedge with its apex on the boundary of the convex hull of S and an O(n2) algorithm for the case of the apex of a wedge coming from the input set S

Decomposing and packing polygons / Dania el-Khechen.

In this thesis, we study three different problems in the field of computational geometry: the partitioning of a simple polygon into two congruent components, the partitioning of squares and rectangles into equal area components while minimizing the perimeter of the cuts, and the packing of the maximum number of squares in an orthogonal polygon. To solve the first problem, we present three polynomial time algorithms which given a simple polygon P partitions it, if possible, into two congruent and possibly nonsimple components P 1 and P 2 : an O ( n 2 log n ) time algorithm for properly congruent components and an O ( n 3 ) time algorithm for mirror congruent components. In our analysis of the second problem, we experimentally find new bounds on the optimal partitions of squares and rectangles into equal area components. The visualization of the best determined solutions allows us to conjecture some characteristics of a class of optimal solutions. Finally, for the third problem, we present three linear time algorithms for packing the maximum number of unit squares in three subclasses of orthogonal polygons: the staircase polygons, the pyramids and Manhattan skyline polygons. We also study a special case of the problem where the given orthogonal polygon has vertices with integer coordinates and the squares to pack are (2 {604} 2) squares. We model the latter problem with a binary integer program and we develop a system that produces and visualizes optimal solutions. The observation of such solutions aided us in proving some characteristics of a class of optimal solutions

MONUMENTAL-IT: A \u27ROBOTIC-WIKI\u27 MONUMENT FOR EMBODIED INTERACTION IN THE INFORMATION WORLD

ABSTRACT Conventional monuments are concrete manifestations of memories without the capacity to reflect individual interpretations of history. In an increasingly digital society, however, there is a need for configurable monuments reflecting our contemporary, open and complex community. “Monumental-IT” reflects the dynamic and inclusive character of our time. Rather than static, Monumental-IT is a dynamic, robotic, intelligent environment reconfigured or “retuned” by citizens and by historical information accumulating on the World Wide Web. This information is periodically “coded,” altering the multi-sensorial physical-digital “Robotic-Wiki” components of Monumental-IT. Monumental-IT is designed to embody a new form of human-robotic interaction evolving from the monument typology. This research is a response to three questions: What is the monument for a world that is increasingly digital and \u27free\u27?; How can intelligent systems \u27creatively\u27 reconcile current conceptualizations of history with monument‐making?; and, What role can intelligent systems and Human Centered Computing (HCC) play in creating significant, meaningful, physical, urban places for collective memories?. This research involves designing, prototyping, and empirically evaluating Monumental-IT. The research employs a mixed-methodological research design which includes: quasi-experimental design, usability, heuristic evaluations, and cognitive walkthroughs as its research methods; and multivariate statistics to validate significance and usability with real users and experts in the domain fields of \u27architectural-robotics\u27 and human factors psychology. Results strongly suggest that the four distinct configurations of the robotic, multi-sensorial Monumental-IT evoke four distinct emotions in users. As well, users interacting with the Monumental-IT prototype evaluate the design as strongly aiding their recollection of human events (here, the history of slavery in the testbed, Charleston, South Carolina, USA). Finally, users overwhelmingly evaluated the Monumental-IT design to be more apt for our increasingly digital society than conventional monument design. Key contributions are: the identification of metrics for evaluating complex digital-physical environments; the advancement of human-robotic interaction via environmental-scaled robotics and multi-sensorial features (colors, sounds and motions); and, the conceptualization of the monument as a cybernetic system

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Comparison of the vocabularies of the Gregg shorthand dictionary and Horn-Peterson's basic vocabulary of business letters

This study is a comparative analysis of the vocabularies of Horn and Peterson's The Basic Vocabulary of Business Letters1 and the Gregg Shorthand Dictionary.2 Both books purport to present a list of words most frequently encountered by stenographers and students of shorthand. The, Basic Vocabulary of Business Letters, published "in answer to repeated requests for data on the words appearing most frequently in business letters,"3 is a frequency list specific to business writing. Although the book carries the copyright date of 1943, the vocabulary was compiled much earlier. The listings constitute a part of the data used in the preparation of the 10,000 words making up the ranked frequency list compiled by Ernest Horn and staff and published in 1926 under the title of A Basic Writing Vocabulary: 10,000 Words Lost Commonly Used in Writing. The introduction to that publication gives credit to Miss Cora Crowder for the contribution of her Master's study at the University of Minnesota concerning words found in business writing. With additional data from supplementary sources, the complete listing represents twenty-six classes of business, as follows 1. Miscellaneous 2. Florists 3. Automobile manufacturers and sales companie

“ONE MORE WAY TO SELL NEW ORLEANS”: AIRBNB AND THE COMMODIFICATION OF AUTHENTICITY THROUGH LOCAL EMOTIONAL LABOR

Since 2014, Airbnb has been the poster-child for an impassioned debate over how to best regulate short-term home rentals (STR’s) in New Orleans, Louisiana. As critical perspectives toward on-demand economic practice become increasingly common, it is important to understand how the impacts of STR platforms like Airbnb extend beyond the realm of what is traditionally conceptualized as the economic (i.e., pressure on housing markets). In this thesis, I explore the ways in which Airbnb recalibrates the spatial and temporal rhythms of everyday neighborhood life for people external to the formal trappings of an STR contract. Drawing in particular on theories of authenticity and feminist political economy, I argue that locals’ emotional labor of “playing host” is necessarily enrolled into the creation of value for Airbnb, and is essential to the reproduction of the platform’s business model and marketing rhetoric