arXiv subjects

Eliot W. Robson

Publications and source records attributed to Eliot W. Robson.

12 recordsLinked to original sources

arXiv2026

A Pressure-Based Diffusion Model for Influence Maximization on Social Networks

In many real-world scenarios, an individual's local social network carries significant influence over the opinions they form and subsequently propagate. In this paper, we propose a novel diffusion model -- the Pressure Threshold model (PT) -- for dynamically simulating the spread of influence through a social network. This model extends the popular Linear Threshold (LT) model by adjusting a node's outgoing influence in proportion to the influence it receives from its activated neighbors. We examine the Influence Maximization (IM) problem under this framework, which involves selecting seed nodes that yield maximal graph coverage after a diffusion process, and describe how the problem manifests under the PT model. Experiments on real-world networks, supported by enhancements to the open-source network-diffusion library CyNetDiff, reveal that greedy IM under PT can yield seed sets distinct from those under LT. Furthermore, the analyses show that densely connected networks amplify pressure effects far more strongly than sparse networks.

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arXiv2026

A Community-Aware Framework for Influence Maximization with Explicit Accounting for Inter-Community Influence

Influence Maximization (IM) seeks to identify a small set of seed nodes in a social network to maximize expected information spread under a diffusion model. While community-based approaches improve scalability by exploiting modular structure, they typically assume independence between communities, overlooking inter-community influence$\unicode{x2014}$a limitation that reduces effectiveness in real-world networks. We introduce Community-IM++, a scalable framework that explicitly models cross-community diffusion through a principled heuristic based on community-based diffusion degree (CDD) and a progressive budgeting strategy. The algorithm partitions the network, computes CDD to prioritize bridging nodes, and allocates seeds adaptively across communities using lazy evaluation to minimize redundant computations. Experiments on large real-world social networks under different edge weight models show that Community-IM++ achieves near-greedy influence spread at up to 100 times lower runtime, while outperforming Community-IM and degree heuristics across budgets and structural conditions. These results demonstrate the practicality of Community-IM++ for large-scale applications such as viral marketing, misinformation control, and public health campaigns, where efficiency and cross-community reach are critical.

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arXiv2025

The Fréchet Distance Unleashed: Approximating a Dog with a Frog

We show that a variant of the continuous Frechet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming can be easily handled via refinement. Combined with a Dijkstra/Prim type algorithm, this leads to a realization of the Frechet distance (i.e., a morphing) that is locally optimal (aka locally correct), that is both easy to compute, and in practice, takes near linear time on many inputs. The new morphing has the property that the leash is always as short as possible. These matchings/morphings are more natural and are better than the ones computed by standard algorithms -- in particular, they handle noise more graciously. This approach should make the Frechet distance more useful for real-world applications. We implemented the new algorithm and various strategies to obtain reasonably fast practical performance. We performed extensive experiments on our new algorithm, and released publicly available (and easily installable and usable) Julia and Python packages. Our algorithms can be used to compute the almost-exact Frechet distance between polygonal curves. Implementations and numerous examples are available here: https://frechet.xyz. We emphasize, however, that the existing state-of-the-art algorithm/implementation in C++ is faster, by several orders of magnitude, than our current algorithm/implementation.

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arXiv2025

The Road to the Closest Point is Paved by Good Neighbors

$\renewcommand{\Re}{\mathbb{R}}$Given a set $P$ of $n$ points in $\Re^d$, and a parameter $\varepsilon \in (0,1)$, we present a new construction of a directed graph $G$, of size $O(n/\varepsilon^d)$, such that $(1+\varepsilon)$-ANN queries can be answered by performing a greedy walk on $G$, repeatedly moving to a neighbor that is (significantly) better than the current point. To the best of our knowledge, this is the first construction of a linear size with no dependency on the spread of the point set. The resulting query time, is $O( \varepsilon^{-d} \log Ψ)$, where $Ψ$ is the spread of $P$. The new construction is surprisingly simple and should be practical.

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arXiv2025

Well-Separated Pairs Decomposition Revisited

We revisit the notion of WSPD (i.e., well-separated pairs-decomposition), presenting a new construction of WSPD for any finite metric space, and show that it is asymptotically instance-optimal in size. Next, we describe a new WSPD construction for the weighted unit-distance metric in the plane, and show a bound $O( \varepsilon^{-2} n \log n)$ on its size, improving by a factor of $1/\varepsilon^2$ over previous work. The new construction is arguably simpler and more elegant. We point out that using WSPD, one can approximate, in near-linear time, the distortion of a bijection between two point sets in low dimensions. As a new application of WSPD, we show how to shortcut a polygonal curve such that its dilation is below a prespecified quantity. In particular, we show a near-linear time algorithm for computing a simple subcurve for a given polygonal curve in the plane so that the new subcurve has no self-intersection.

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arXiv2025

The Analytic Arc Cover Problem and its Applications to Contiguous Art Gallery, Polygon Separation, and Shape Carving

We show the following problems are in $\textsf{P}$: 1. The contiguous art gallery problem -- a variation of the art gallery problem where each guard can protect a contiguous interval along the boundary of a simple polygon. This was posed at the open problem session at CCCG '24 by Thomas C. Shermer. 2. The polygon separation problem for line segments -- For two sets of line segments $S_1$ and $S_2$, find a minimum-vertex convex polygon $P$ that completely contains $S_1$ and does not contain or cross any segment of $S_2$. 3. Minimizing the number of half-plane cuts to carve a 3D polytope. To accomplish this, we study the analytic arc cover problem -- an interval set cover problem over the unit circle with infinitely many implicitly-defined arcs, given by a function.

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arXiv2025

Improving the average dilation of a metric graph by adding edges

For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to augment $G$ with $k$ additional edges to reduce the maximum dilation. In this note, we consider a variant of this problem where the goal is to reduce the average dilation for pairs of points in $G$. We provide an $O(k)$ approximation algorithm for this problem, matching the approximation ratio given by prior work for the maximum dilation variant.

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arXiv2025

No-dimensional Tverberg Partitions Revisited

$ \newcommand{\epsA}{\Mhδ} \newcommand{\Re}{\mathbb{R}} \newcommand{\reals}{\mathbb{R}} \newcommand{\SetX}{\mathsf{X}} \renewcommand¶{P} \newcommand{\diam}Δ \newcommand{\Mh}[1]{#1} \newcommand{\query}{q} \newcommand{\eps}{\varepsilon} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\IntRange}[1]{[ #1 ]} \newcommand{\Space}{\overline{\mathsf{m}}} \newcommand{\pth}[2][\!]{#1\left({#2}\right)} \newcommand{\polylog}{\mathrm{polylog}} \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\pt}{p} \newcommand{\distY}[2]{\left\| {#1} - {#2} \right\|} \newcommand{\PP}{P} \newcommand{\ptq}{q} \newcommand{\pts}{s}$Given a set $P \subset \Re^d$ of $n$ points, with diameter $\diam$, and a parameter $\epsA \in (0,1)$, it is known that there is a partition of $P$ into sets $P_1, \ldots, P_t$, each of size $O(1/\epsA^2)$, such that their convex-hulls all intersect a common ball of radius $\epsA \diam$. We prove that a random partition, with a simple alteration step, yields the desired partition, resulting in a (randomized) linear time algorithm. We also provide a deterministic algorithm with running time $O( dn \log n)$. Previous proofs were either existential (i.e., at least exponential time), or required much bigger sets. In addition, the algorithm and its proof of correctness are significantly simpler than previous work, and the constants are slightly better. We also include a number of applications and extensions using the same central ideas. For example, we provide a linear time algorithm for computing a ``fuzzy'' centerpoint, and prove a no-dimensional weak $\eps$-net theorem with an improved constant.

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arXiv2024

Carving Polytopes with Saws in 3D

We investigate the problem of carving an $n$-face triangulated three-dimensional polytope using a tool to make cuts modelled by either a half-plane or sweeps from an infinite ray. In the case of half-planes cuts, we present a deterministic algorithm running in $O(n^2)$ time and a randomized algorithm running in $O(n^{3/2+\varepsilon})$ expected time for any $\varepsilon>0$. In the case of cuts defined by sweeps of infinite rays, we present an algorithm running in $O(n^5)$ time.

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arXiv2024

Fractional Budget Allocation for Influence Maximization under General Marketing Strategies

We consider the fractional influence maximization problem, i.e., identifying users on a social network to be incentivized with potentially partial discounts to maximize the influence on the network. The larger the discount given to a user, the higher the likelihood of its activation (adopting a new product or innovation), who then attempts to activate its neighboring users, causing a cascade effect of influence through the network. Our goal is to devise efficient algorithms that assign initial discounts to the network's users to maximize the total number of activated users at the end of the cascade, subject to a constraint on the total sum of discounts given. In general, the activation likelihood could be any non-decreasing function of the discount, whereas, our focus lies on the case when the activation likelihood is an affine function of the discount, potentially varying across different users. As this problem is shown to be NP-hard, we propose and analyze an efficient (1-1/e)-approximation algorithm. Furthermore, we run experiments on real-world social networks to show the performance and scalability of our method.

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arXiv2024

CyNetDiff -- A Python Library for Accelerated Implementation of Network Diffusion Models

In recent years, there has been increasing interest in network diffusion models and related problems. The most popular of these are the independent cascade and linear threshold models. Much of the recent experimental work done on these models requires a large number of simulations conducted on large graphs, a computationally expensive task suited for low-level languages. However, many researchers prefer the use of higher-level languages (such as Python) for their flexibility and shorter development times. Moreover, in many research tasks, these simulations are the most computationally intensive task, so it would be desirable to have a library for these with an interface to a high-level language with the performance of a low-level language. To fill this niche, we introduce CyNetDiff, a Python library with components written in Cython to provide improved performance for these computationally intensive diffusion tasks.

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arXiv2023

On the Width of the Regular $n$-Simplex

Consider the regular $n$-simplex $Δ_n$ - it is formed by the convex-hull of $n+1$ points in Euclidean space, with each pair of points being in distance exactly one from each other. We prove an exact bound on the width of $Δ_n$ which is $\approx \sqrt{2/n}$. Specifically, $ \mathrm{width}(Δ_n) = \sqrt{\frac{2}{n + 1}}$ if $n$ is odd, and $ \mathrm{width}(Δ_n) = \sqrt{\frac{2(n+1)}{n(n+2)}} $ if $n$ is even. While this bound is well known [GK92, Ale77], we provide a self-contained elementary proof that might (or might not) be of interest.

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