The Niceness of Unique Sink Orientations

Random Edge is the most natural randomized pivot rule for the simplex algorithm. Considerable progress has been made recently towards fully understanding its behavior. Back in 2001, Welzl introduced the concepts of \emph{reachmaps} and \emph{niceness} of Unique Sink Orientations (USO), in an effort to better understand the behavior of Random Edge. In this paper, we initiate the systematic study of these concepts. We settle the questions that were asked by Welzl about the niceness of (acyclic) USO. Niceness implies natural upper bounds for Random Edge and we provide evidence that these are tight or almost tight in many interesting cases. Moreover, we show that Random Edge is polynomial on at least $n^{\Omega(2^n)}$ many (possibly cyclic) USO. As a bonus, we describe a derandomization of Random Edge which achieves the same asymptotic upper bounds with respect to niceness and discuss some algorithmic properties of the reachmap.Comment: An extended abstract appears in the proceedings of Approx/Random 201

The Niceness of Unique Sink Orientations

Random Edge is the most natural randomized pivot rule for the simplex algorithm. Considerable progress has been made recently towards fully understanding its behavior. Back in 2001, Welzl introduced the concepts of reachmaps and niceness of Unique Sink Orientations (USO), in an effort to better understand the behavior of Random Edge. In this paper, we initiate the systematic study of these concepts. We settle the questions that were asked by Welzl about the niceness of (acyclic) USO. Niceness implies natural upper bounds for Random Edge and we provide evidence that these are tight or almost tight in many interesting cases. Moreover, we show that Random Edge is polynomial on at least n^{Omega(2^n)} many (possibly cyclic) USO. As a bonus, we describe a derandomization of Random Edge which achieves the same asymptotic upper bounds with respect to niceness

Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results

A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin-Courant rule for preferences single-peaked on trees. We show that the egalitarian version of this problem admits a polynomial-time algorithm. For the utilitarian version, we prove that winner determination remains NP-hard, even for the Borda scoring function; however, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We also consider several other optimization criteria for trees: for some we obtain polynomial-time algorithms, while for others we show NP-hardness results.Comment: 44 pages, extends works published at AAAI 2016 and IJCAI 201

Complexity Theory, Game Theory, and Economics: The Barbados Lectures

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v

Controlling involvement to promote confidence in palliative care decisions - a grounded theory from the patient\u27s perspective

Decision making in the context of palliative care is particularly complex given the unpredictable illness trajectories experienced by patients and the number of individuals who may be part of the decision making process. This grounded theory study explored and described from the perspective of patients with advanced illness, their experiences of making care decisions. A review of literature at the commencement of the study indicated that there was a lack of evidence to support the best way of ascertaining patient\u27s preferences for involvement in decisions in a palliative care context and almost no research to guide clinicians about the involvement of patients and families in decision making

Taking A Knee To “whiteness” In Urban Teacher Education: An Abolitionist Stance

In a qualitative narrative study of 11 urban teacher education faculty who teach courses that prepare teacher candidates for field immersions in metro-urban schools, I problematized “whiteness” by asking participants what it meant to them in the contexts of their work in contact zones were teacher candidates and K-12 students meet. The research was shaped as an abolitionist justice project (Tuck & Yang, 2018, p. 8) and considered how “whiteness” might be deconstructed and decentered in urban teacher education. Participants described whiteness as both fixed phenotype and historical and social construct which causes harm and which requires intervention. In scenarios where the harm of whiteness was mitigated for non-white K-12 students and teacher candidates, participants described themselves in supportive rather than authoritative educational roles. The study reflects upon what might constitute one or more forms of abolitionist praxis which might have the utility to dismantle systemic white supremacy as well as to cease and desist in the oppression of children

Cold War New York: Postmodernism, Lyricism, And Queer Aesthetics In 1970s New York Poetry

This thesis explores the poetry of Joe Brainard and Anne Waldman, two poets of the critically neglected second-generation New York school. I argue that Brainard and Waldman help define the emerging discourse of postmodern poetry through their attention to cold war culture of the 1970s, countercultural ideologies, and poetic form. Both Brainard and Waldman enact a poetics of vulnerability in their work, situating themselves as wholly unique from their late-modernist predecessors. In doing so, they help engender a poetics concerned not only with the intellectual stakes but with the cultural environment they are forced to navigate. Chapter 1 explores Brainard\u27s I remember and the Bolinas journal, arguing that his queer phenomenological approach to writing defines the early forms of postmodernism. Chapter 2 investigates the feminist poetics of Waldman and her engagement with performance and politics as a way to offer a new kind of poetics intent on plurality. The conclusion of this thesis looks at the notion of democracy and the postmodern poet, questioning the necessity for a political poetics and its utility in literary, cultural, and American history

A journey to understand dual language and the bilingual world: An autoethnography of a bilingual program director in an urban district

This research represents a personalized account of the complexities, interpretations, and reflections on the life-long epistemological development of a bilingual program director currently implementing a dual language program in an urban school district. Using myself as a subject and a researcher in cultural, personal, and professional contexts provided the impetus for this self-study. Through the lens of a mother, daughter, sister, teacher, principal, and bilingual program director, I have chronicled and traced the epistemological conception of the assets that guide my advocacy in the academic realm of bilingual education. As an autoethnography, this study invites the reader to experience the research through the lens of their own personal perspective, finding pieces of themselves in the collective consciousness shared by all inhabitants of the bilingual world. While every individual has their own unique life experience and cultural development, autoethnography encourages an authentic conversation between the researcher and the reader (Davies, 2007; Delamont, 2009; Ellis, 1996, 2004; Ellis & Bochner, 2000, 2006; Preston, 2011). The experiences I have encountered, the challenges I have faced, and the interpretations derived from those experiences strengthen my understanding of where my cultural strengths come from, as well as provide insight into how those strengths allow me to choose the appropriate pedagogies and navigate the administrative challenges that accompany the position of a bilingual program director in an urban district