arXiv subjects

Bingbing Hu

Publications and source records attributed to Bingbing Hu.

4 recordsLinked to original sources

arXiv2025

Hardness of Dynamic Tree Edit Distance and Friends

String Edit Distance is a more-than-classical problem whose behavior in the dynamic setting, where the strings are updated over time, is well studied. A single-character substitution, insertion, or deletion can be processed in time $\tilde{\mathcal{O}}(n w)$ when operation costs are positive integers bounded by $w$ [Charalampopoulos, Kociumaka, Mozes, CPM 2020][Gorbachev, Kociumaka, STOC 2025]. If the weights are further uniform (insertions and deletions have equal cost), also an $\tilde{\mathcal{O}}(n \sqrt{n})$-update time algorithm exists [Charalampopoulos, Kociumaka, Mozes, CPM 2020]. This is a substantial improvement over the static $\mathcal{O}(n^2)$ algorithm when $w \ll n$ or when we are dealing with uniform weights. In contrast, for inherently related problems such as Tree Edit Distance, Dyck Edit Distance, and RNA Folding, it has remained unknown whether it is possible to devise dynamic algorithms with an advantage over the static algorithm. In this paper, we resolve this question by showing that (weighted) Tree Edit Distance, Dyck Edit Distance, and RNA Folding admit no dynamic speedup: under well-known fine-grained assumptions we show that the best possible algorithm recomputes the solution from scratch after each update. Furthermore, we prove a quadratic per-update lower bound for unweighted Tree Edit Distance under the $k$-Clique Conjecture. This provides the first separation between dynamic unweighted String Edit Distance and unweighted Tree Edit Distance, problems whose relative difficulty in the static setting is still open.

cs.DS↗

arXiv2024

Learnable Infinite Taylor Gaussian for Dynamic View Rendering

Capturing the temporal evolution of Gaussian properties such as position, rotation, and scale is a challenging task due to the vast number of time-varying parameters and the limited photometric data available, which generally results in convergence issues, making it difficult to find an optimal solution. While feeding all inputs into an end-to-end neural network can effectively model complex temporal dynamics, this approach lacks explicit supervision and struggles to generate high-quality transformation fields. On the other hand, using time-conditioned polynomial functions to model Gaussian trajectories and orientations provides a more explicit and interpretable solution, but requires significant handcrafted effort and lacks generalizability across diverse scenes. To overcome these limitations, this paper introduces a novel approach based on a learnable infinite Taylor Formula to model the temporal evolution of Gaussians. This method offers both the flexibility of an implicit network-based approach and the interpretability of explicit polynomial functions, allowing for more robust and generalizable modeling of Gaussian dynamics across various dynamic scenes. Extensive experiments on dynamic novel view rendering tasks are conducted on public datasets, demonstrating that the proposed method achieves state-of-the-art performance in this domain. More information is available on our project page(https://ellisonking.github.io/TaylorGaussian).

cs.CV↗

arXiv2024

Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems

Most of the known tight lower bounds for dynamic problems are based on the Online Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and understood as some more popular hypotheses in fine-grained complexity. It would be desirable to base hardness of dynamic problems on a more believable hypothesis. We propose analogues of the OMv Hypothesis for variants of matrix multiplication that are known to be harder than Boolean product in the offline setting, namely: equality, dominance, min-witness, min-max, and bounded monotone min-plus products. These hypotheses are a priori weaker assumptions than the standard (Boolean) OMv Hypothesis. Somewhat surprisingly, we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.

cs.CC↗

arXiv2023

Connectivity Oracles for Predictable Vertex Failures

The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan--Pettie STOC'10; Long--Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph $G=(V,E)$ and a set of vertices predicted to fail $\widehat{D} \subseteq V$ of size $d=|\widehat{D}|$, preprocesses it in time $\tilde{O}(d|E|)$ and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices $\widehat{D} \triangle D = (\widehat{D} \setminus D) \cup (D \setminus \widehat{D})$ of size $\eta = |\widehat{D} \triangle D|$, process it in time $\tilde{O}(\eta^4)$, and after that answer connectivity queries in $G \setminus D$ in time $O(\eta)$. Viewed from another perspective, our data structure provides an improvement over the state of the art for the \emph{fully dynamic subgraph connectivity problem} in the \emph{sensitivity setting} [Henzinger--Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.

cs.DS↗