Approximating acyclicity parameters of sparse hypergraphs

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database theory and artificial intelligence. In this paper, we study the approximability of (generalized, fractional) hyper treewidth of sparse hypergraphs where the criterion of sparsity reflects the sparsity of their incidence graphs. Our first step is to prove that the (generalized, fractional) hypertree width of a hypergraph H is constant-factor sandwiched by the treewidth of its incidence graph, when the incidence graph belongs to some apex-minor-free graph class. This determines the combinatorial borderline above which the notion of (generalized, fractional) hypertree width becomes essentially more general than treewidth, justifying that way its functionality as a hypergraph acyclicity measure. While for more general sparse families of hypergraphs treewidth of incidence graphs and all hypertree width parameters may differ arbitrarily, there are sparse families where a constant factor approximation algorithm is possible. In particular, we give a constant factor approximation polynomial time algorithm for (generalized, fractional) hypertree width on hypergraphs whose incidence graphs belong to some H-minor-free graph class

On the Optimality of Pseudo-polynomial Algorithms for Integer Programming

In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP) is an important step in numerous algorithms and it is important to obtain an understanding of the precise complexity of this problem as a function of natural parameters of the input. The classic pseudo-polynomial time algorithm of Papadimitriou [J. ACM 1981] for instances of (IP) with a constant number of constraints was only recently improved upon by Eisenbrand and Weismantel [SODA 2018] and Jansen and Rohwedder [ArXiv 2018]. We continue this line of work and show that under the Exponential Time Hypothesis (ETH), the algorithm of Jansen and Rohwedder is nearly optimal. We also show that when the matrix $A$ is assumed to be non-negative, a component of Papadimitriou's original algorithm is already nearly optimal under ETH. This motivates us to pick up the line of research initiated by Cunningham and Geelen [IPCO 2007] who studied the complexity of solving (IP) with non-negative matrices in which the number of constraints may be unbounded, but the branch-width of the column-matroid corresponding to the constraint matrix is a constant. We prove a lower bound on the complexity of solving (IP) for such instances and obtain optimal results with respect to a closely related parameter, path-width. Specifically, we prove matching upper and lower bounds for (IP) when the path-width of the corresponding column-matroid is a constant.Comment: 29 pages, To appear in ESA 201

Historical Butches: Lesbian Experience and Masculinity in Bryher\u27s Historical Fiction

This project analyzes three of Bryher\u27s historical novels, while also providing background on the shadowy figure of Bryher herself. Looking at Gate to the Sea, Roman Wall, and Ruan, each serves to represent lesbianism in a variety of coded or metaphorical ways. Various geographical locations or landscapes serve to either represent or depict homosexual desire, and also construct queer spaces for characters to traverse. Limited scholarship exists on any of Bryher\u27s works, particularly that which looks at lesbian sexuality. The genre Bryher writes in allows for a cross-writing of lesbian characters, or gendering lesbian characters as male, and displays awareness of masculinity as a social construct. Throughout each of her novels, Bryher manipulates form to encode homosexual desire and nonheteronormative relationships

Electron scattering in HCl: An improved nonlocal resonance model

We present an improved nonlocal resonance model for electron-HCl collisions. The short-range part of the model is fitted to ab initio electron-scattering eigenphase sums calculated using the Schwinger multichannel method, while the long-range part is based on the ab initio potential-energy curve of the bound anion HCl-. This model significantly improves the agreement of nonlocal resonance calculations with recent absolute experimental data on dissociative electron attachment cross sections for HCl and DCl. It also partly resolves an inconsistency in the temperature effect in dissociative electron attachment to HCl present in the literature. Finally, the present model reproduces all qualitative structures observed previously in elastic scattering and vibrational-excitation cross sections