Theory & Algorithms · Computer Science & AI
Computational Complexity
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343 papers, from 31 August 2026 to 5 November 2026: 282 arXiv preprints and 61 OpenAlex records.
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Newest papers, page 5
Unconditional Lower Bounds for the Fredman--Khachiyan Algorithms for Monotone Boolean Duality Testing
We prove unconditional lower bounds on the number of recursive calls made by the two algorithms of Fredman and Khachiyan (1996) for monotone Boolean duality testing, as a function of the explicit…Communication Complexity of Integer Matrix Singularity
Alice and Bob hold complementary halves of the columns of an $n\times n$ matrix of $k$-bit integers and decide whether it is singular over $\mathbb Q$.Searching for binary orientable sequences
An aperiodic binary orientable sequence is a finite sequence of zeros and ones for which, for some integer $n$, all the subsequences of $n$ consecutive symbols, read either forwards or backwards…Structure and Exact Certification of Nonnegative Tensor Decompositions
We study the structure and exact certification of nonnegative tensor decompositions supplied through rational factor matrices.Deterministic Root-Finding over Finite Fields with Elliptic Curves
Finding the roots of a polynomial over a finite field $\mathbb F_q$ in deterministic polynomial time is a long-standing open problem.Near-Quadratic Time Multivariate Polynomial Interpolation
Let $\F$ be a finite field.Tight Bounds on the Randomized Communication Complexity of Vector-in-Subspace
We prove that the randomized communication complexity of Vector-in-Subspace in $\mathbb R^n$ with error at most $1/3$ is $Θ(\sqrt n)$.A Quasipolynomial Algorithm for $\ell_\infty$ Contractions
We give an algorithm for computing an $\eps$-approximate fixed point of any $d$-dimensional nonexpansion with respect to the $\ell_\infty$ norm in time $\log(1/\eps)^{O(\log^2 d)}$.Temporal Exploration and Rendezvous via Weisfeiler-Leman Colorings
Temporal graphs are graphs whose edge relation changes in discrete time steps.A 55-Addition Rank-23 Scheme for $3\times3$ Matrix Multiplication via Exact Two-Sided Minimization
We give a scheme that multiplies two $3\times3$ matrices with 23 multiplications and 55 additions over any ring, one addition below the previous record of 56 (Sun, 2026) and the first below 56 for…Fixed Sets and the Hardness of Computing Correlated Equilibria
We show that computing an approximate correlated equilibrium of a polytope game is PPAD-complete, and thus polynomial-time equivalent to finding a Nash equilibrium.Subjective Valuations Make It Hard to be Fair: The Complexity of Resource Allocation to Groups of Agents
We study the parameterized complexity of finding an EF1 allocation of indivisible items in the group-sharing setting, which has received increasing attention in recent years.Hidden parabolic subgroups of $\mathrm{GL}_n$ over finite chain rings
We give a bounded-error quantum polynomial-time algorithm for finding hidden parabolic subgroups of $\mathrm{GL}_n(R)$ over any effectively presented finite chain ring $R$.Two $\operatorname{ReLU}$ Layers is All You Need
We prove that every $\operatorname{ReLU}$ network can be exactly simulated by a $\operatorname{ReLU}$ network with two hidden layers.Amplified Pruning and Path Selectors for Deterministic Radio Gossiping
We study deterministic gossiping in unknown strongly connected directed radio networks with $n$ vertices, $m$ arcs, and distinct identifiers in $[N]$, where $N=n^{\mathcal O(1)}$.A General Construction of Strict Models in HoTT
Homotopy type theory (HoTT) provides a natural setting for studying the metatheory of type theory, as it comes with additional extensionality principles compared to ordinary Martin-Löf type theory.Internalizing Chain-of-thought into Looped Transformers
Chain-of-thought (CoT) enables constant-bit-size transformers to perform general-purpose computation through generated tokens (Li and Wang, 2025a), whereas looped transformers carry out the same…Bidirectionality is Necessary in Cellular Machines for Exact-Arrival Multi-Agent Path Finding
On ranked directed acyclic graphs coupled by vertex conflicts we study exact-arrival multi-agent path finding (departure and arrival pinned in place and time) posed as a distributed output task…Orienting mixed graphs for reachability pairs: When the all pairs setting is easier than the general one
Given a mixed graph $G$ and an ordered pair $(u,v)$ of vertices in $V(G)$, we say that an orientation $\vec{G}$ of $G$ satisfies $(u,v)$ if $v$ is reachable from $u$ in $\vec{G}$.A Short Note on Algorithms For The Noisy $k$-XOR Problem
This mostly expository note studies the sample-noise regimes in which the testing problem for noisy $k$-XOR in dimension $n$ can be efficiently solved.