The Atlantic Mind: Zephaniah Kingsley, Slavery, and the Politics of Race in the Atlantic World

Enlightenment philosophers had long feared the effects of crisscrossing boundaries, both real and imagined. Such fears were based on what they considered a brutal ocean space frequented by protean shape-shifters with a dogma of ruthless exploitation and profit. This intellectual study outlines the formation and fragmentation of a fluctuating worldview as experienced through the circum-Atlantic life and travels of merchant, slaveowner, and slave trader Zephaniah Kingsley during the Era of Revolution. It argues that the process began from experiencing the costs of loyalty to the idea of the British Crown and was tempered by the pervasiveness of violence, mobility, anxiety, and adaptation found in the booming Atlantic markets of the Caribbean during the Haitian Revolution. Tracing Kingsley’s manipulations of identity and race through his peripatetic journey serves to go beyond the infinite masks of his self-invention and exposes the deeply imbedded transatlantic dimensions of power

The Atlantic Legacies of Zephaniah Kingsley: Benevolence, Bondage, and Proslavery Fictions in the Age of Emancipation

Nineteenth-century slaveholders of the Atlantic master class had many reasons to be concerned with the future. In a world ushered in with the aid of the Haitian Revolution, slave revolts in these sensitive times seemed to erupt with increased frequency, leaving greater destruction in their wakes. Abolition and a transatlantic antislavery movement appeared as determined crusades to bring an end not only to human suffering in black chattel slavery but to the system’s unsurpassed wealth. In this era of sweeping changes a vision of British West Indian society without slaves was first debated and then made a reality on 1 August 1834. In the months and years that followed British Emancipation, there was much to debate in the postslavery situation from what seemed like all quarters. Abolitionists scrutinized production levels and profits. Slaveowners clamored for compensation for losing property in persons and, on the whole, feared the complete breakdown of Caribbean society that was sure to follow. In recent years scholars have noted the ways in which the institution of slavery and the practice of slaveholding were quite diverse across time and space. Less attention has been given to variations within slavery’s demise and to the master class’s attempts to control the postslavery landscapes of the Atlantic world. The following dissertation examines the legacies of Zephaniah Kingsley, a planter from northeast Florida who confronted the Age of Emancipation in the last decade of his life with an ambitious proslavery colonization scheme in 1830s Haiti. Establishing a large plantation there stocked with some of his former slaves, Kingsley conducted his elaborate efforts under benevolent pretenses in order to manipulate public opinion but worried about his own sordid actions in the long march of history. Since his death in 1843, generations continue to be haunted by Kingsley’s enigmatic life and the tragedies of his exploits. In studying the ambitious events that occupied his final years, we can better understand the ways in which slaveholders like Kingsley confronted the prospect of emancipation and launched new mechanisms of control

Polylogarithmic Approximation for Generalized Minimum Manhattan Networks

Given a set of $n$ terminals, which are points in $d$-dimensional Euclidean space, the minimum Manhattan network problem (MMN) asks for a minimum-length rectilinear network that connects each pair of terminals by a Manhattan path, that is, a path consisting of axis-parallel segments whose total length equals the pair's Manhattan distance. Even for $d=2$, the problem is NP-hard, but constant-factor approximations are known. For $d \ge 3$, the problem is APX-hard; it is known to admit, for any \eps > 0, an O(n^\eps)-approximation. In the generalized minimum Manhattan network problem (GMMN), we are given a set $R$ of $n$ terminal pairs, and the goal is to find a minimum-length rectilinear network such that each pair in $R$ is connected by a Manhattan path. GMMN is a generalization of both MMN and the well-known rectilinear Steiner arborescence problem (RSA). So far, only special cases of GMMN have been considered. We present an $O(\log^{d+1} n)$-approximation algorithm for GMMN (and, hence, MMN) in $d \ge 2$ dimensions and an $O(\log n)$-approximation algorithm for 2D. We show that an existing $O(\log n)$-approximation algorithm for RSA in 2D generalizes easily to $d>2$ dimensions.Comment: 14 pages, 5 figures; added appendix and figure

New Algorithms for Maximum Disjoint Paths Based on Tree-Likeness

We study the classical NP-hard problems of finding maximum-size subsets from given sets of k terminal pairs that can be routed via edge-disjoint paths (MaxEDP) or node-disjoint paths (MaxNDP) in a given graph. The approximability of MaxEDP/NDP is currently not well understood; the best known lower bound is Omega(log^{1/2 - varepsilon} n), assuming NP not subseteq ZPTIME(n^{poly log n}). This constitutes a significant gap to the best known approximation upper bound of O(n^1/2) due to Chekuri et al. (2006) and closing this gap is currently one of the big open problems in approximation algorithms. In their seminal paper, Raghavan and Thompson (Combinatorica, 1987) introduce the technique of randomized rounding for LPs; their technique gives an O(1)-approximation when edges (or nodes) may be used by O(log n/log log n) paths. In this paper, we strengthen the above fundamental results. We provide new bounds formulated in terms of the feedback vertex set number r of a graph, which measures its vertex deletion distance to a forest. In particular, we obtain the following. - For MaxEDP, we give an O(r^0.5 log^1.5 kr)-approximation algorithm. As r<=n, up to logarithmic factors, our result strengthens the best known ratio O(n^0.5) due to Chekuri et al. - Further, we show how to route Omega(opt) pairs with congestion O(log(kr)/log log(kr)), strengthening the bound obtained by the classic approach of Raghavan and Thompson. - For MaxNDP, we give an algorithm that gives the optimal answer in time (k+r)^O(r)n. This is a substantial improvement on the run time of 2^kr^O(r)n, which can be obtained via an algorithm by Scheffler. We complement these positive results by proving that MaxEDP is NP-hard even for r=1, and MaxNDP is W[1]-hard for parameter r. This shows that neither problem is fixed-parameter tractable in r unless FPT = W[1] and that our approximability results are relevant even for very small constant values of r

A PTAS for Euclidean TSP with Hyperplane Neighborhoods

In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN is known to be APX-hard, which gives rise to studying more tractable special cases of the problem. In this paper, we focus on the fundamental special case of regions that are hyperplanes in the $d$-dimensional Euclidean space. This case contrasts the much-better understood case of so-called fat regions. While for $d=2$ an exact algorithm with running time $O(n^5)$ is known, settling the exact approximability of the problem for $d=3$ has been repeatedly posed as an open question. To date, only an approximation algorithm with guarantee exponential in $d$ is known, and NP-hardness remains open. For arbitrary fixed $d$, we develop a Polynomial Time Approximation Scheme (PTAS) that works for both the tour and path version of the problem. Our algorithm is based on approximating the convex hull of the optimal tour by a convex polytope of bounded complexity. Such polytopes are represented as solutions of a sophisticated LP formulation, which we combine with the enumeration of crucial properties of the tour. As the approximation guarantee approaches $1$, our scheme adjusts the complexity of the considered polytopes accordingly. In the analysis of our approximation scheme, we show that our search space includes a sufficiently good approximation of the optimum. To do so, we develop a novel and general sparsification technique to transform an arbitrary convex polytope into one with a constant number of vertices and, in turn, into one of bounded complexity in the above sense. Hereby, we maintain important properties of the polytope

Gap-ETH-Tight Approximation Schemes for Red-Green-Blue Separation and Bicolored Noncrossing Euclidean Travelling Salesman Tours

In this paper, we study problems of connecting classes of points via noncrossing structures. Given a set of colored terminal points, we want to find a graph for each color that connects all terminals of its color with the restriction that no two graphs cross each other. We consider these problems both on the Euclidean plane and in planar graphs. On the algorithmic side, we give a Gap-ETH-tight EPTAS for the two-colored traveling salesman problem as well as for the red-blue-green separation problem (in which we want to separate terminals of three colors with two noncrossing polygons of minimum length), both on the Euclidean plane. This improves the work of Arora and Chang (ICALP 2003) who gave a slower PTAS for the simpler red-blue separation problem. For the case of unweighted plane graphs, we also show a PTAS for the two-colored traveling salesman problem. All these results are based on our new patching procedure that might be of independent interest. On the negative side, we show that the problem of connecting terminal pairs with noncrossing paths is NP-hard on the Euclidean plane, and that the problem of finding two noncrossing spanning trees is NP-hard in plane graphs.Comment: 36 pages, 15 figures (colored