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Balancing the Spread of Two Opinions in Sparse Social Networks
arXiv:2105.10184v3 Announce Type: replace Abstract: Inspired by the famous Target Set Selection problem, we propose a new discrete model to simultaneously spread two opinions within a social network and perform an initial study of its complexity. Here, we are given a social network, a seed-set of agents for each opinion, two thresholds for each agent, a budget, and a number of rounds. The first threshold represents the willingness of an agent to adopt an opinion if the agent has no opinion...
$O(n +f(k))$: Truly Linear FPT
Announce Type: new Abstract: Parameterized complexity has always been concerned with practical computing: by confining combinatorial explosion to a secondary parameter $k$, one can uncover why and how many NP-hard problems are effectively tackled in practice. Today, however, the scale of data has changed: scientists study Big Data, which is so large that even quadratic dependence in the total input size $n$ is unaffordable. Therefore, what constitutes a practical algorithm has also changed.
bbsolver: A Unified Error-Bounded Spatiotemporal Optimization Solver for Key Timing and Topology-Consistent Vector Paths
arXiv:2606.09741v1 Announce Type: new Abstract: Dense sampling records what an animation system actually evaluated, but it produces a poor final representation: every sampled frame can become a key, edit handles become noisy, and animated vector paths remain hard to adjust. Existing reducers usually treat the two axes separately: animation-curve reducers reduce key timing, while curve and path simplifiers reduce geometry. When applied independently to animated paths, these methods can break...
PlayStation Architecture
Supporting imagery A quick introduction Sony knew that 3D hardware could get very messy to develop for. Thus, their debuting console will keep its design simple and practical… Although this may come at a cost!
On graph products and multi-word-representability
arXiv:2603.29629v4 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under six standard graph products: the lexicographic, Cartesian, rooted, corona, tensor, and strong products. For the Cartesian and rooted products, we show that $\mu(G_1 \square G_2)=\mu(G_1 \diamond G_2)=\max\{\mu(G_1),\mu(G_2)\}$. For the corona product, we prove that...
On graph products and multi-word-representability
arXiv:2603.29629v3 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under four standard graph products: the lexicographic, Cartesian, rooted, and corona products.
Making Graphics Like it's 1993
Personal website and blog. Catlantean 3D is a side-project I've been slowly building in my spare time for over a year, and I intend to release it on Steam next year. My goal was to build a complete, shippable first-person shooter using techniques that were common in the early 90s, while allowing myself the luxury of using a modern compiler and a platform abstraction layer.
On the Duke--Erd\H{o}s--R\"odl Problem at the One-Third Threshold
Announce Type: cross Abstract: Let $G$ be an $n$-vertex graph with $e(G)\ge n^2/ k$. We prove a self-contained internal short-cycle core theorem at the threshold $k\le n^{1/3}$: the graph $G$ contains a subgraph $H_6$ with $\Omega(n^2/ k^3)$ edges in which every two distinct edges lie together on a cycle of length at most $6$ contained in $H_6$, and a subgraph $H_8$ with $\Omega(n^2/k^2)$ edges in which every two distinct edges lie together on a cycle of length at most $8$ contained in...