Insertion-Only Dynamic Connectivity in General Disk Graphs

Let $S \subseteq \mathbb{R}^2$ be a set of $n$ \emph{sites} in the plane, so that every site $s \in S$ has an \emph{associated radius} $r_s > 0$. Let $D(S)$ be the \emph{disk intersection graph} defined by $S$, i.e., the graph with vertex set $S$ and an edge between two distinct sites $s, t \in S$ if and only if the disks with centers $s$, $t$ and radii $r_s$, $r_t$ intersect. Our goal is to design data structures that maintain the connectivity structure of $D(S)$ as $S$ changes dynamically over time. We consider the incremental case, where new sites can be inserted into $S$. While previous work focuses on data structures whose running time depends on the ratio between the smallest and the largest site in $S$, we present a data structure with $O(\alpha(n))$ amortized query time and $O(\log^6 n)$ expected amortized insertion time.Comment: 7 pages, 6 figures. Presented at EuroCG 2023. This version corrects a missing log-factor in the insertion tim

Dynamic Connectivity in Disk Graphs

Let S ⊆ R2 be a set of n sites in the plane, so that every site s ∈ S has an associated radius rs > 0. Let D(S) be the disk intersection graph defined by S, i.e., the graph with vertex set S and an edge between two distinct sites s, t ∈ S if and only if the disks with centers s, t and radii rs , rt intersect. Our goal is to design data structures that maintain the connectivity structure of D(S) as sites are inserted and/or deleted in S. First, we consider unit disk graphs, i.e., we fix rs = 1, for all sites s ∈ S. For this case, we describe a data structure that has O(log2 n) amortized update time and O(log n/ log log n) query time. Second, we look at disk graphs with bounded radius ratio Ψ, i.e., for all s ∈ S, we have 1 ≤ rs ≤ Ψ, for a parameter Ψ that is known in advance. Here, we not only investigate the fully dynamic case, but also the incremental and the decremental scenario, where only insertions or only deletions of sites are allowed. In the fully dynamic case, we achieve amortized expected update time O(Ψ log4 n) and query time O(log n/ log log n). This improves the currently best update time by a factor of Ψ. In the incremental case, we achieve logarithmic dependency on Ψ, with a data structure that has O(α(n)) amortized query time and O(log Ψ log4 n) amortized expected update time, where α(n) denotes the inverse Ackermann function. For the decremental setting, we first develop an efficient decremental disk revealing data structure: given two sets R and B of disks in the plane, we can delete disks from B, and upon each deletion, we receive a list of all disks in R that no longer intersect the union of B. Using this data structure, we get decremental data structures with a query time of O(log n/ log log n) that supports deletions in O(n log Ψ log4 n) overall expected time for disk graphs with bounded radius ratio Ψ and O(n log5 n) overall expected time for disk graphs with arbitrary radii, assuming that the deletion sequence is oblivious of the internal random choices of the data structures

Sea level fall during glaciation stabilized atmospheric CO2 by enhanced volcanic degassing

Paleo-climate records and geodynamic modelling indicate the existence of complex interactions between glacial sea level changes, volcanic degassing and atmospheric CO2, which may have modulated the climate system’s descent into the last ice age. Between ∼85 and 70 kyr ago, during an interval of decreasing axial tilt, the orbital component in global temperature records gradually declined, while atmospheric CO2, instead of continuing its long-term correlation with Antarctic temperature, remained relatively stable. Here, based on novel global geodynamic models and the joint interpretation of paleo-proxy data as well as biogeochemical simulations, we show that a sea level fall in this interval caused enhanced pressure-release melting in the uppermost mantle, which may have induced a surge in magma and CO2 fluxes from mid-ocean ridges and oceanic hotspot volcanoes. Our results reveal a hitherto unrecognized negative feedback between glaciation and atmospheric CO2 predominantly controlled by marine volcanism on multi-millennial timescales of ∼5,000–15,000 years

How do farmers learn from extension services? Evidence from Malawi

Though extension services have long since proved their value to agricultural production and farmer prosperity, their record in sub‐Saharan Africa has been mixed. To study the impact of such programs on farmers' learning about agricultural technologies, we implemented a quasi‐randomized controlled trial and collected detailed panel data among Malawian farmers. Based on those findings, we develop a two‐stage learning framework, in which farmers formulate yield expectations before deciding on how much effort to invest in learning about these processes. Using data centered on farmer beliefs, knowledge, and constraints, we find evidence that beliefs about potential yields hinge on first‐hand and local experience, and that these beliefs significantly impact learning efforts. Consistent with this, we find that farmers who participated in season‐long, farmer‐led demonstration plot cultivation plan to adopt more components of new multi‐component technology, compared to farmers who were invited to attend only field‐day events

Seeding Science, Courting Conclusions: Reexamining the Intersection of Science, Corporate Cash, and the Law

Social scientists have expressed strong views on corporate influences over science, but most attention has been devoted to broad, Black/White arguments, rather than to actual mechanisms of influence. This paper summarizes an experience where involvement in a lawsuit led to the discovery of an unexpected mechanism: A large corporation facing a multibillion-dollar court judgment quietly provided generous funding to well-known scientists (including at least one Nobel prize winner) who would submit articles to "open," peer-reviewed journals, so that their "unbiased science" could be cited in an appeal to the Supreme Court. On balance, the corporation's most effective techniques of influence may have been provided not by overt pressure, but by encouraging scientists to continue thinking of themselves as independent and impartial

Nearest-Neighbor Decompositions of Drawings

P_c. We show that it is NP-complete to decide whether ? can be drawn as the union of c ? 3 nearest-neighbor graphs, even when no two segments cross. We show that for c = 2, it is NP-complete in the general setting and polynomial-time solvable when no two segments cross. We show the existence of an O(log n)-approximation algorithm running in subexponential time for partitioning ? into a minimum number of nearest-neighbor graphs. As a main tool in our analysis, we establish the notion of the conflict graph for a drawing ?. The vertices of the conflict graph are the connected components of ?, with the assumption that each connected component is the nearest neighbor graph of its vertices, and there is an edge between two components U and V if and only if the nearest neighbor graph of U ? V contains an edge between a vertex in U and a vertex in V. We show that string graphs are conflict graphs of certain planar drawings. For planar graphs and complete k-partite graphs, we give additional, more efficient constructions. We furthermore show that there are subdivisions of non-planar graphs that are not conflict graphs. Lastly, we show a separator lemma for conflict graphs

On the Maximum Number of Crossings in Star-Simple Drawings of Kn with No Empty Lens

A star-simple drawing of a graph is a drawing in which adjacent edges do not cross. In contrast, there is no restriction on the number of crossings between two independent edges. When allowing empty lenses (a face in the arrangement induced by two edges that is bounded by a 2-cycle), two independent edges may cross arbitrarily many times in a star-simple drawing. We consider star-simple drawings of Kn with no empty lens. In this setting we prove an upper bound of 3((n−4)!) on the maximum number of crossings between any pair of edges. It follows that the total number of crossings is finite and upper bounded by n!.ISSN:0302-9743ISSN:1611-334

Simplifying Non-simple Fan-Planar Drawings

A drawing of a graph is fan-planar if the edges intersecting a common edge a share a vertex A on the same side of a. More precisely, orienting e arbitrarily and the other edges towards A results in a consistent orientation of the crossings. So far, fan-planar drawings have only been considered in the context of simple drawings, where any two edges share at most one point, including endpoints. We show that every non-simple fan-planar drawing can be redrawn as a simple fan-planar drawing of the same graph while not introducing additional crossings. Combined with previous results on fan-planar drawings, this yields that n-vertex-graphs having such a drawing can have at most 6.5n edges and that the recognition of such graphs is NP-hard. We thereby answer an open problem posed by Kaufmann and Ueckerdt in 2014.ISSN:0302-9743ISSN:1611-334