On the Threshold of Intractability

We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-complete, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics, 113(1):109--128, 2001). On the positive side, we show the problem admits a quadratic vertex kernel. Furthermore, we give a subexponential time parameterized algorithm solving Threshold Editing in $2^{O(\surd k \log k)} + \text{poly}(n)$ time, making it one of relatively few natural problems in this complexity class on general graphs. These results are of broader interest to the field of social network analysis, where recent work of Brandes (ISAAC, 2014) posits that the minimum edit distance to a threshold graph gives a good measure of consistency for node centralities. Finally, we show that all our positive results extend to the related problem of Chain Editing, as well as the completion and deletion variants of both problems

Tuning of Human Modulation Filters Is Carrier-Frequency Dependent

Licensed under the Creative Commons Attribution License

Induced Disjoint Paths in Circular-Arc Graphs in Linear Time

The Induced Disjoint Paths problem is to test whether a graph G with k distinct pairs of vertices (si,ti) contains paths P1,…,Pk such that Pi connects si and ti for i=1,…,k, and Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their ends) for 1≤

Standardised data on initiatives—STARDIT: Beta version

Background and objective: There is currently no standardised way to share information across disciplines about initiatives, including fields such as health, environment, basic science, manufacturing, media and international development. All problems, including complex global problems such as air pollution and pandemics require reliable data sharing between disciplines in order to respond effectively. Current reporting methods also lack information about the ways in which different people and organisations are involved in initiatives, making it difficult to collate and appraise data about the most effective ways to involve different people. The objective of STARDIT (Standardised Data on Initiatives) is to address current limitations and inconsistencies in sharing data about initiatives. The STARDIT system features standardised data reporting about initiatives, including who has been involved, what tasks they did, and any impacts observed. STARDIT was created to help everyone in the world find and understand information about collective human actions, which are referred to as ‘initiatives’. STARDIT enables multiple categories of data to be reported in a standardised way across disciplines, facilitating appraisal of initiatives and aiding synthesis of evidence for the most effective ways for people to be involved in initiatives. This article outlines progress to date on STARDIT; current usage; information about submitting reports; planned next steps and how anyone can become involved. Method: STARDIT development is guided by participatory action research paradigms, and has been co-created with people from multiple disciplines and countries. Co-authors include cancer patients, people affected by rare diseases, health researchers, environmental researchers, economists, librarians and academic publishers. The co-authors also worked with Indigenous peoples from multiple countries and in partnership with an organisation working with Indigenous Australians. Results and discussion: Over 100 people from multiple disciplines and countries have been involved in co-designing STARDIT since 2019. STARDIT is the first open access web-based data-sharing system which standardises the way that information about initiatives is reported across diverse fields and disciplines, including information about which tasks were done by which stakeholders. STARDIT is designed to work with existing data standards. STARDIT data will be released into the public domain (CC0) and integrated into Wikidata; it works across multiple languages and is both human and machine readable. Reports can be updated throughout the lifetime of an initiative, from planning to evaluation, allowing anyone to be involved in reporting impacts and outcomes. STARDIT is the first system that enables sharing of standardised data about initiatives across disciplines. A working Beta version was publicly released in February 2021 (ScienceforAll.World/STARDIT). Subsequently, STARDIT reports have been created for peer-reviewed research in multiple journals and multiple research projects, demonstrating the usability. In addition, organisations including Cochrane and Australian Genomics have created prospective reports outlining planned initiatives. Conclusions: STARDIT can help create high-quality standardised information on initiatives trying to solve complex multidisciplinary global problems

Open problems on graph coloring for special graph classes.

For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c:V→{1,2,…}c:V→{1,2,…} such that c(u)≠c(v)c(u)≠c(v) for every edge uv∈Euv∈E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring

The Temporal Signature of Memories: Identification of a General Mechanism for Dynamic Memory Replay in Humans

Reinstatement of dynamic memories requires the replay of neural patterns that unfold over time in a similar manner as during perception. However, little is known about the mechanisms that guide such a temporally structured replay in humans, because previous studies used either unsuitable methods or paradigms to address this question. Here, we overcome these limitations by developing a new analysis method to detect the replay of temporal patterns in a paradigm that requires participants to mentally replay short sound or video clips. We show that memory reinstatement is accompanied by a decrease of low-frequency (8 Hz) power, which carries a temporal phase signature of the replayed stimulus. These replay effects were evident in the visual as well as in the auditory domain and were localized to sensory-specific regions. These results suggest low-frequency phase to be a domain-general mechanism that orchestrates dynamic memory replay in humans

Deleting edges to restrict the size of an epidemic: a new application for treewidth

Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most k edges from a given input graph (of small treewidth) so that the resulting graph avoids a set FF of forbidden subgraphs; of particular interest is the problem of determining whether it is possible to delete at most k edges so that the resulting graph has no connected component of more than h vertices, as this bounds the worst-case size of an epidemic. While even this special case of the problem is NP-complete in general (even when h=3h=3 ), we provide evidence that many of the real-world networks of interest are likely to have small treewidth, and we describe an algorithm which solves the general problem in time 2O(|F|wr)n2O(|F|wr)n  on an input graph having n vertices and whose treewidth is bounded by a fixed constant w, if each of the subgraphs we wish to avoid has at most r vertices. For the special case in which we wish only to ensure that no component has more than h vertices, we improve on this to give an algorithm running in time O((wh)2wn)O((wh)2wn) , which we have implemented and tested on real datasets based on cattle movements