Computational Complexity Papers of the Week

We develop a common framework for classical simulation of boson and fermion sampling under thermal loss, including pure loss.

This paper investigates a time-dependent urban hazardous materials (hazmat) transportation routing optimization problem, where vehicles depart from a distribution center to serve a set of customers.

In particular, we first strengthen existing NP-hardness results by showing that the problem remains NP-complete on graphs of bounded tree-depth and also on cactus graphs which are one vertex deletion away from being path forests. Motivated by this (severe) hardness, we study several other parameterizations of the problem and obtain FPT algorithms parameterized by vertex integrity (generalizing a recent FPT algorithm parameterized by vertex cover by Fomin, Fraigniaud, and Golovach [TCS 2024]) and by distance to clique, as well as FPT approximation algorithms parameterized by clique-cover and cluster vertex deletion.

We initiate the study of middle-bit predictors: functions that take as input a string with one missing bit and try to predict that bit.

However, its real‐time measurement capability is severely restricted by the substantial data throughput and computational cost, hindering its practical deployment. To overcome this limitation, we propose a real‐time 3D measurement method based on Hartley‐domain parallel single‐pixel imaging (HPSI).

To this end, we propose a novel Multi-Agentic AI framework in which each device decomposes its local workload across three cooperating: Agent 2 performs data preprocessing, including WGAN-based oversampling to correct class imbalance; Agent 1 performs data distribution, applying a vertical federated learning (VFL) partitioning scheme to address the unequal data distribution that typically affects FL-based IoT systems; and Agent 3 performs classification, training a deep autoencoder and an MLP on the resulting features while keeping the computational load on each device manageable.

We prove that the problem remains $CLS$-complete even when the coefficients are encoded in unary.

We study community search when each vertex has its own tolerance for differences in position.

For every $d$ and $r$ we determine the expected movement needed to sort $n$ keys: it is $n^{\beta}$ up to polylogarithmic factors, where $\beta=1+D^{r-1}/(D^{r}-(D-1)^{r})$ and $D=2d$, falling from $n^{2}$ at $r=1$ to $n^{1+1/(2d)}$ with unlimited rounds.

We determine it on $\ell_1$ products of betweenness-free metrics, those with no point between two others, a class containing every Hamming graph.

In this work, we present a simple and interpretable framework called "Compressed Oracle Duality," which extends the Compressed Oracle method for space-bounded algorithms.

This paper provides a replicable experiment that compares the performance of XGBoost and a hybrid CNN–LSTM–Transformer model on CICIDS2017 flow-level dataset.

We prove that any linear $3$-query locally correctable code $C \colon \mathbb{F}_2^k \to \mathbb{F}_2^n$ with constant correction radius must have length $n \geq 2^{\Omega(\sqrt{k})}$.

We determine the information complexity of matrix multiplication over finite fields under independent uniform inputs, up to a universal additive constant.

However, existing methods often suffer from high computational complexity, poor noise resistance, and redundant feature extraction, which limits measurement accuracy and efficiency. To address these limitations, this paper proposes a density-geometry collaborative constraint method that integrates geometric feature analysis with an optimization algorithm.

To this end, we introduce a capped Horvitz--Thompson estimator with uniformly bounded discrete derivatives on the $p$-biased cube.

For general sampling and counting algorithms, we establish a robust fine-grained reduction from SAT without assuming a lower bound on SAT's running time.

We study the randomized classical query complexity of cyclic Forrelation, a cyclic analogue of $k$-Forrelation [AA15, STOC'15; BS21, STOC'21].

For every fixed dimension $d$, we give an algorithm for $m$ queries, $n$ key-value pairs, and additive error $\varepsilon$, with expected time $ \widetilde{\mathrm{O}}\bigl((mn)^{k/(k+1)}+m+n\bigr),\qquad k=\lfloor d/2\rfloor.

We study the gradient query complexity of sampling from a density $\pi(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $\beta$-Lipschitz gradient but need not be convex.