Graph editing problems with extended regularity constraints

© 2017 Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of parameterized complexity as the problems have rich parameter ecologies. In this paper we examine generalisations of the notion of editing a graph to obtain a regular subgraph. In particular we extend the notion of regularity to include two variants of edge-regularity along with the unifying constraint of strong regularity. We present a number of results, with the central observation that these problems retain the general complexity profile of their regularity-based inspiration: when the number of edits k and the maximum degree r are taken together as a combined parameter, the problems are tractable (i.e. in FPT), but are otherwise intractable. We also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph. In this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k+r parameterization

A Proof Checking View of Parameterized Complexity

The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it also gives strong non-approximability results. In this paper we initiate the study of proof checking within the scope of Parameterized Complexity. In particular we adapt and extend the PCP[n log log n, n log log n] result of Feige et al. to several parameterized classes, and discuss some corollaries

Distribution, morphology, and genetic affinities of dwarf embedded Fucus populations from the Northwest Atlantic Ocean

Dwarf embedded Fucus populations in the Northwest Atlantic Ocean are restricted to the upper intertidal zone in sandy salt marsh environments; they lack holdfasts and are from attached parental populations of F. spiralis or F. spiralis x F. vesiculosus hybrids after breakage and entanglement with halophytic marsh grasses. Dwarf forms are dichotomously branched, flat, and have a mean overall length and width of 20.3 and 1.3 mm, respectively. Thus, they are longer than Irish (mean 9.3 mm) and Alaskan (mean 15.0 mm) populations identified as F cottonii. Reciprocal transplants of different Fucus taxa in a Maine salt marsh confirm that F spiralis can become transformed into dwarf embedded thalli within the high intertidal zone, while the latter can grow into F. s. ecad lutarius within the mid intertidal zone. Thus, vertical transplantation can modify fucoid morphology and result in varying ecads. Microsatellite markers indicate that attached F spiralis and F vesiculosus are genetically distinct, while dwarf forms may arise via hybridization between the two taxa. The ratio of intermediate to species-specific-genotypes decreased with larger thalli. Also, F s. ecad lutarius consists of a mixture of intermediate and pure genotypes, while dwarf thalli show a greater frequency of hybrids

A Decision Support System for Student Transfer Advising

Many students start their academic careers at community colleges. After a year or two, they transfer to a university to complete their undergraduate degrees. Students who make poor course selections at community colleges may find that some of their course credits do not transfer to the university programs of their choice. A decision support system was developed to help community college students (1) understand the structure of university undergraduate degree programs, and (2) identify community college courses that meet university requirements. The system is designed to be easy to use and attractive for the typical community college student. It was consiructed by a team of three undergraduate MIS students over the course of a single semester using a Windows-based hypermedia tool

Syntax error based quantification of the learning progress of the novice programmer

© 2018 Association for Computing Machinery. Recent data-driven research has produced metrics for quantifying a novice programmer’s error profile, such as Jadud’s error quotient. However, these metrics tend to be context dependent and contain free parameters. This paper reviews the caveats of such metrics and proposes a more general approach to developing a metric. The online implementation of the proposed metric is publicly available at http://online-analysis-demo.herokuapp.com/

ArAl: An Online Tool for Source Code Snapshot Metadata Analysis

© 2019 Association for Computing Machinery. Several systems that collect data from students' problem solving processes exist. Within computing education research, such data has been used for multiple purposes, ranging from assessing students' problem solving strategies to detecting struggling students. To date, however, the majority of the analysis has been conducted by individual researchers or research groups using case by case methodologies. Our belief is that with increasing possibilities for data collection from students' learning process, researchers and instructors will benefit from ready-made analysis tools. In this study, we present ArAl, an online machine learning based platform for analyzing programming source code snapshot data. The benefit of ArAl is two-fold. The computing education researcher can use ArAl to analyze the source code snapshot data collected from their own institute. Also, the website provides a collection of well-documented machine learning and statistics based tools to investigate possible correlation between different variables. The presented web-portal is available at online-analysisdemo. herokuapp.com. This tool could be applied in many different subject areas given appropriate performance data

Separating sets of strings by finding matching patterns is almost always hard

© 2017 Elsevier B.V. We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in understanding the complexity of genetic algorithms. We show that the basic problem of finding a small set of patterns that match one set of strings but do not match any string in a second set is difficult (NP-complete, W[2]-hard when parameterized by the size of the pattern set, and APX-hard). We then perform a detailed parameterized analysis of the problem, separating tractable and intractable variants. In particular we show that parameterizing by the size of pattern set and the number of strings, and the size of the alphabet and the number of strings give FPT results, amongst others

On the Parameterised Complexity of Induced Multipartite Graph Parameters

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable.Comment: 9 pages, 0 figure

On the Parameterised Complexity of Induced Multipartite Graph Parameters

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable.Comment: 9 pages, 0 figure

On the Feasibility of Maintenance Algorithms in Dynamic Graphs

Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly disconnected) graph over time naturally leads to the important complexity question: is it better to calculate a new solution from scratch or to adapt the known solution on the prior graph to quickly provide a solution of guaranteed quality for the changed graph? In this paper, we demonstrate that the former is the best approach in some cases, but that there are cases where the latter is feasible. We prove that, under certain conditions, hard problems cannot even be approximated in any reasonable complexity bound --- i.e., even with a large amount of time, having a solution to a very similar graph does not help in computing a solution to the current graph. To achieve this, we formalize the idea as a maintenance algorithm. Using r-Regular Subgraph as the primary example we show that W[1]-hardness for the parameterized approximation problem implies the non-existence of a maintenance algorithm for the given approximation ratio. Conversely we show that Vertex Cover, which is fixed-parameter tractable, has a 2-approximate maintenance algorithm. The implications of NP-hardness and NPO-hardness are also explored