Lucian Bicsi | Search arXiv

arXiv2026

Incremental Minimum Spanning Trees on a Napkin

In the incremental minimum spanning forest problem, weighted edges arrive one at a time. After each insertion we must report the edge that leaves the minimum spanning forest, and queries ask for the bottleneck distance of two vertices: the smallest possible maximum edge cost on a path between them. Link-cut trees solve both in $O(\log n)$ amortized time. In 2021 we wrote the folklore BottleneckTree, a short competitive-programming structure that stores one parent pointer and one cost per vertex, and conjectured that it also runs in $O(\log n)$ amortized time. We show that this conjecture is false: on a family of inputs, its amortized cost per operation is $Ω(\sqrt{n})$. We then present a structure with the same state, two arrays and a single loop, and prove that it runs in $O(\log n)$ amortized time per insertion and per query. Unlike the AM-tree of Ding, Gu and Sun, which attains the same bound, it stores no subtree sizes and maintains no balance invariant. For a connected graph with distinct costs, the structure can be viewed as an implicit link-cut tree on the Kruskal reconstruction tree: each rotation corresponds to exactly one preferred-child change, and each skip acts on a stale path-parent pointer. In experiments it is 1.3-2.1 times faster than the folklore BottleneckTree on insertions, up to 480 times faster on its adversarial input, and 6.3-16 times faster than an explicit link-cut tree.

cs.DS↗

arXiv2023

JEDI: Joint Expert Distillation in a Semi-Supervised Multi-Dataset Student-Teacher Scenario for Video Action Recognition

We propose JEDI, a multi-dataset semi-supervised learning method, which efficiently combines knowledge from multiple experts, learned on different datasets, to train and improve the performance of individual, per dataset, student models. Our approach achieves this by addressing two important problems in current machine learning research: generalization across datasets and limitations of supervised training due to scarcity of labeled data. We start with an arbitrary number of experts, pretrained on their own specific dataset, which form the initial set of student models. The teachers are immediately derived by concatenating the feature representations from the penultimate layers of the students. We then train all models in a student-teacher semi-supervised learning scenario until convergence. In our efficient approach, student-teacher training is carried out jointly and end-to-end, showing that both students and teachers improve their generalization capacity during training. We validate our approach on four video action recognition datasets. By simultaneously considering all datasets within a unified semi-supervised setting, we demonstrate significant improvements over the initial experts.

cs.CV↗