Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm

In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level Planarity, where vertices have to lie on given horizontal lines indicating a hierarchy, and Clustered Planarity, where we additionally draw the boundaries of clusters which recursively group the vertices in a crossing-free manner. Despite receiving significant amount of attention and substantial theoretical progress on these problems, only very few of the found solutions have been put into practice and evaluated experimentally. In this paper, we describe our implementation of the recent quadratic-time algorithm by Bl\"asius et al. [TALG Vol 19, No 4] for solving the problem Synchronized Planarity, which can be seen as a common generalization of several constrained planarity problems, including the aforementioned ones. Our experimental evaluation on an existing benchmark set shows that even our baseline implementation outperforms all competitors by at least an order of magnitude. We systematically investigate the degrees of freedom in the implementation of the Synchronized Planarity algorithm for larger instances and propose several modifications that further improve the performance. Altogether, this allows us to solve instances with up to 100 vertices in milliseconds and instances with up to 100 000 vertices within a few minutes.Comment: to appear in Proceedings of ALENEX 202

Experimental Comparison of PC-Trees and PQ-Trees

PQ-trees and PC-trees are data structures that represent sets of linear and circular orders, respectively, subject to constraints that specific subsets of elements have to be consecutive. While equivalent to each other, PC-trees are conceptually much simpler than PQ-trees; updating a PC-tree so that a set of elements becomes consecutive requires only a single operation, whereas PQ-trees use an update procedure that is described in terms of nine transformation templates that have to be recursively matched and applied. Despite these theoretical advantages, to date no practical PC-tree implementation is available. This might be due to the original description by Hsu and McConnell [Hsu et al., 2003] in some places only sketching the details of the implementation. In this paper, we describe two alternative implementations of PC-trees. For the first one, we follow the approach by Hsu and McConnell, filling in the necessary details and also proposing improvements on the original algorithm. For the second one, we use a different technique for efficiently representing the tree using a Union-Find data structure. In an extensive experimental evaluation we compare our implementations to a variety of other implementations of PQ-trees that are available on the web as part of academic and other software libraries. Our results show that both PC-tree implementations beat their closest fully correct competitor, the PQ-tree implementation from the OGDF library [Markus Chimani et al., 2014; Leipert, 1997], by a factor of 2 to 4, showing that PC-trees are not only conceptually simpler but also fast in practice. Moreover, we find the Union-Find-based implementation, while having a slightly worse asymptotic runtime, to be twice as fast as the one based on the description by Hsu and McConnell

Parameterized Complexity of Simultaneous Planarity

Given $k$ input graphs $G_1, \dots ,G_k$, where each pair $G_i$, $G_j$ with $i \neq j$ shares the same graph $G$, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks whether there exists a planar drawing for each input graph such that all drawings coincide on $G$. While SEFE is still open for the case of two input graphs, the problem is NP-complete for $k \geq 3$ [Schaefer, JGAA 13]. In this work, we explore the parameterized complexity of SEFE. We show that SEFE is FPT with respect to $k$ plus the vertex cover number or the feedback edge set number of the the union graph $G^\cup = G_1 \cup \dots \cup G_k$. Regarding the shared graph $G$, we show that SEFE is NP-complete, even if $G$ is a tree with maximum degree 4. Together with a known NP-hardness reduction [Angelini et al., TCS 15], this allows us to conclude that several parameters of $G$, including the maximum degree, the maximum number of degree-1 neighbors, the vertex cover number, and the number of cutvertices are intractable. We also settle the tractability of all pairs of these parameters. We give FPT algorithms for the vertex cover number plus either of the first two parameters and for the number of cutvertices plus the maximum degree, whereas we prove all remaining combinations to be intractable.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

Synchronized planarity with applications to constrained planarity problems

We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. Synchronized Planarity then asks whether the graph admits a crossing-free embedding into the plane such that the orders of edges around synchronized vertices are consistent. We show, on the one hand, that Synchronized Planarity can be solved in quadratic time, and, on the other hand, that it serves as a powerful modeling language that lets us easily formulate several constrained planarity problems as instances of Synchronized Planarity. In particular, this lets us solve Clustered Planarity in quadratic time, where the most efficient previously known algorithm has an upper bound of O(n⁸)

Distinguishing wet from dry age-related macular degeneration using three-dimensional computer-automated threshold Amsler grid testing

Background/aims: With the increased efficacy of current therapy for wet age-related macular degeneration (AMD), better ways to detect wet AMD are needed. This study was designed to test the ability of three-dimensional contrast threshold Amsler grid (3D-CTAG) testing to distinguish wet AMD from dry AMD. Methods: Conventional paper Amsler grid and 3D-CTAG tests were performed in 90 eyes: 63 with AMD (34 dry, 29 wet) and 27 controls. Qualitative comparisons were based upon the three-dimensional shapes of central visual field (VF) defects. Quantitative analyses considered the number and volume of the three-dimensional defects. Results: 25/34 (74%) dry AMD and 6/29 (21%) wet AMD eyes had no distortions on paper Amsler grid. Of these, 5/25 (20%) dry and 6/6 (100%) wet (p=0.03) AMD eyes exhibited central VF defects with 3D-CTAG. Wet AMD displayed stepped defects in 16/28 (57%) eyes, compared with only 2/34 (6%) of dry AMD eyes (p=0.002). All three volumetric indices of VF defects were two- to four-fold greater in wet than dry AMD (p<0.006). 3D-CTAG had 83.9% positive and 90.6% negative predictive values for wet AMD. Conclusions: 3D-CTAG has a higher likelihood of detecting central VF defects than conventional Amsler grid, especially in wet AMD. Wet AMD can be distinguished from dry AMD by qualitative and quantitative 3D-CTAG criteria. Thus, 3D-CTAG may be useful in screening for wet AMD, quantitating disease severity, and providing a quantitative outcome measure of therapy

Green function Retrieval and Time-reversal in a Disordered World

We apply the theory of multiple wave scattering to two contemporary, related topics: imaging with diffuse correlations and stability of time-reversal of diffuse waves, using equipartition, coherent backscattering and frequency speckles as fundamental concepts.Comment: 1 figur

Questionnaire study to gain an insight into the manufacturing and fitting process of artificial eyes in children: an ocularist perspective

Purpose To gain an insight into the manufacturing and fitting of artificial eyes in children and potential improvements to the process. Method An online qualitative survey was distributed to 39 ocularists/prosthetists in Europe and Canada. Participants were recruited through purposive sampling, specifically maximum variation sampling from the researcher’s contacts and an online search. Results The findings highlighted the current impression technique as being the most difficult yet most important part of the current process for both the ocularist and child patient. Negatively affecting obtaining a good impression, the child patients distress can be reduced by their parents by providing encouragement, reassurance, practicing the insertion and removal of the artificial eye and being matter of fact. Whilst improvements to the current process provided mixed views, the incorporation of current technology was perceived as not being able to meet the requirements to produce aesthetically pleasing artificial eyes. Conclusion The current artificial eye process can be seen as an interaction with its success being dependent on the child patient’s acceptance and adjustment which is dependent on the factors associated to the process. Investigation into the needs of the patient and whether technology can improve the process are the next steps in its advancement

'Throughout my life I've had people walk all over me': trauma in the lives of violent men

In this article we present original qualitative data gathered during prolonged ethnographic fieldwork with violent men in deindustrialised communities in the north of England. We use the data as an empirical platform for a theoretical exploration of the symbolism and subjectivising influences of traumatic life experiences in these men’s biographies. We conclude by making the tentative suggestion that there is a complex and mediated causal link between traumatic experience and a deep subjective commitment to aggression and violence in adulthood

Reply to comment by Karnauskas et al. on "Equatorial Pacific coral geochemical records show recent weakening of the Walker circulation"

In our paper describing a new coral record from Butaritari, we hypothesized that comparing the temporal trends in our records to coral records from farther east in the equatorial Pacific may support the evidence for a weakening of a Walker circulation, documented elsewhere in the literature [Power and Smith, 2007; Tokinaga et al., 2012]. Weakening of the Walker circulation is expected under global warming due to an imbalance in the rate of change in different aspects of the hydrological cycle [Vecchi and Soden, 2007]. We thank Karnauskas et al. [2015] for recognizing the value of our Butaritari coral climate reconstruction, and we appreciate their critique of our study. The Karnauskas et al. [2015] analyses strengthen our argument regarding the utility of interisland coral-proxy derived sea surface temperature (SST) gradients as a Walker circulation metric, but we disagree with their interpretation of decadal variability in our records. Here we provide additional analyses, which confirm that our reconstruction [Carilli et al., 2014] shows a long-term weakening of the Walker circulation over 1972-1998. We also document that significant decadal variations in Walker circulation strength, and for particular choices of start and end years over which trends are calculated, are able to show slight Walker strengthening. Overall, we conclude that Walker circulation variations are more nuanced than either our original publication [Carilli et al., 2014] or the subsequent Karnauskas et al. [2015] comment would suggest. Karnauskas et al. [2015] also provide a detailed analysis of Equatorial Undercurrent (EUC) activity near the Gilbert Islands and argue that the EUC does not strongly affect Butaritari. Our original publication did not claim to find significant EUC/Butaritari linkages, and we appreciate the diligence of Karnauskas et al. [2015] for ruling this out as a possibility

Equatorial Pacific coral geochemical records show recent weakening of the Walker Circulation

Equatorial Pacific ocean-atmosphere interactions affect climate globally, and a key component of the coupled system is the Walker Circulation, which is driven by sea surface temperature (SST) gradients across the equatorial Pacific. There is conflicting evidence as to whether the SST gradient and Walker Circulation have strengthened or weakened over the late twentieth century. We present new records of SST and sea surface salinity (SSS) spanning 1959-2010 based on paired measurements of Sr/Ca and δ18O in a massive Porites coral from Butaritari atoll in the Gilbert Islands, Republic of Kiribati, in the central western equatorial Pacific. The records show 2-7 year variability correlated with the El Niño-Southern Oscillation (ENSO) and corresponding shifts in the extent of the Indo-Pacific Warm Pool, and decadal-scale signals related to the Pacific Decadal Oscillation and the Pacific Warm Pool Index. In addition, the Butaritari coral records reveal a small but significant increase in SST (0.39°C) from 1959 to 2010 with no accompanying change in SSS, a trend that persists even when ENSO variability is removed. In contrast, larger increases in SST and SSS are evident in coral records from the equatorial Pacific Line Islands, located east of Butaritari. Taken together, the equatorial Pacific coral records suggest an overall reduction in the east-west SST and SSS gradient over the last several decades, and a recent weakening of the Walker Circulation