On Structural Parameterizations of Hitting Set: Hitting Paths in Graphs Using 2-SAT

Hitting Set is a classic problem in combinatorial optimization. Its input consists of a set system F over a finite universe U and an integer t; the question is whether there is a set of t elements that intersects every set in F. The Hitting Set problem parameterized by the size of the solution is a well-known W[2]-complete problem in parameterized complexity theory. In this paper we investigate the complexity of Hitting Set under various structural parameterizations of the input. Our starting point is the folklore result that Hitting Set is polynomial-time solvable if there is a tree T on vertex set U such that the sets in F induce connected subtrees of T. We consider the case that there is a treelike graph with vertex set U such that the sets in F induce connected subgraphs; the parameter of the problem is a measure of how treelike the graph is. Our main positive result is an algorithm that, given a graph G with cyclomatic number k, a collection P of simple paths in G, and an integer t, determines in time 2^{5k} (|G| +|P|)^O(1) whether there is a vertex set of size t that hits all paths in P. It is based on a connection to the 2-SAT problem in multiple valued logic. For other parameterizations we derive W[1]-hardness and para-NP-completeness results.Comment: Presented at the 41st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2015. (The statement of Lemma 4 was corrected in this update.

Properties of quasi-periodic pulsations in solar flares from a single active region

We investigate the properties of a set of solar flares originating from a single active region (AR) that exhibit QPPs, and look for signs of the QPP periods relating to AR properties. The AR studied, best known as NOAA 12192, was unusually long-lived and produced 181 flares. Data from the GOES, EVE, Fermi, Vernov and NoRH observatories were used to determine if QPPs were present in the flares. For the soft X-ray GOES and EVE data, the time derivative of the signal was used. Power spectra of the time series data (without any form of detrending) were inspected, and flares with a peak above the 95% confidence level in the spectrum were labelled as having candidate QPPs. The confidence levels were determined taking account of uncertainties and the possible presence of red noise. AR properties were determined using HMI line of sight magnetograms. A total of 37 flares (20% of the sample) show good evidence of having QPPs, and some of the pulsations can be seen in data from multiple instruments and in different wavebands. The QPP periods show a weak correlation with the flare amplitude and duration, but this may be due to an observational bias. A stronger correlation was found between the QPP period and duration of the QPP signal, which can be partially but not entirely explained by observational constraints. No correlations were found with the AR area, bipole separation, or average magnetic field strength. The fact that a substantial fraction of the flare sample showed evidence of QPPs using a strict detection method with minimal processing of the data demonstrates that these QPPs are a real phenomenon, which cannot be explained by the presence of red noise or the superposition of multiple unrelated flares. The lack of correlation between the QPP periods and AR properties implies that the small-scale structure of the AR is important, and/or that different QPP mechanisms act in different cases.Comment: 23 pages, 57 figures. Accepted for publication by Astronomy & Astrophysic

Criminal Justice Sentencing Policy Statement

This policy statement, put forth by the NCCD Board of directors, is a revision of our 1992 "Statement on Criminal Sentencing." We reviewed the developments of the past 13 years and outlined NCCD's positions on issues such as mandatory minimums and the death penalty

Asset Building for Social Change: Pathways to Large-Scale Impact

Provides an in-depth examination of current and historic initiatives, in an effort to discern patterns of successful scaling up from among Ford's Assets Program portfolios worldwide

A Profile of the Working Poor, 2011

In 2011, according to the U.S. Census Bureau, about 46.2 million people, or 15.0 percent of the nation’s population, lived below the official poverty level.1 Although the poor were primarily children and adults who had not participated in the labor force during the year, according to data from the Bureau of Labor Statistics, 10.4 million individuals were among the “working poor” in 2011; this measure was little changed from 2010. The working poor are persons who spent at least 27 weeks in the labor force (that is, working or looking for work) but whose incomes still fell below the official poverty level. In 2011, the working-poor rate—the ratio of the working poor to all individuals in the labor force for at least 27 weeks— was 7.0 percent, slightly below the previous year’s figure (7.2 percent). (See tables A and 1 and chart 1.