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$O(n +f(k))$: 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.
Deterministic Monotone Min-Plus Product and Convolution
arXiv:2605.07150v2 Announce Type: replace Abstract: The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone non-decreasing sequence of integers from $\{1,\dots,n\}$, and the goal is to compute their Min-Plus product, defined as the $n\times n$ matrix $C$ with $C_{i,j} = \min_{k}\{A_{i,k} + B_{k,j}\}$. The fastest...
Counting Distinct (Non-)Crossing Substrings in Optimal Time
Announce Type: replace Abstract: Let $w$ be a string of length $n$. The problem of counting factors crossing a position -- Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Lecroq, and Rytter, 2021] -- asks to count the number $\mathcal{C}(w,k)$ (resp. $\mathcal{N}(w,k)$) of distinct substrings in $w$ that have occurrences containing (resp.
Bounds for Single-Error-Correcting Analog Codes
arXiv:2606.03011v1 Announce Type: new Abstract: We study single-error correction for analog codes over $\mathbb{R}$. A key performance measure is the parameter $\Gamma_2(\mathcal{C})$, which quantifies the minimum separation required between large outlying errors that need to be located/corrected and bounded tolerable perturbations. We prove that every real linear $[n,n-2]$ code $\mathcal{C}$ satisfies \[ \Gamma_2(\mathcal{C})\ge \frac{1}{\sin^2(\pi/2n)}. This resolves Roth's open problem on...
SIRT7 regulates dosage compensation and safeguards the female X chromosome
Abstract Sirtuins are deacetylases implicated in stress responses and longevity in mammals1,2. Although their differential impact on disease for the two sexes has been noted3,4,5,6,7, the underlying reasons are unclear. Here, using Sirt7 as a model in mice, we examine the mechanisms leading to sex differences and find that Sirt7−/− female mice have decreased fitness throughout their lifespan.
Rectangular Matrix Multiplication in the Low-Bandwidth Model
arXiv:2606.04652v1 Announce Type: new Abstract: We study rectangular matrix multiplication in the low-bandwidth model of distributed computing. There are $n$ computers; initially the input matrices are distributed evenly between computers, and in each communication round every computer can send and receive an $O(\log n)$-bit message. Eventually each computer must output its designated part of the product matrix.
Almost balanced ordered biclique covering of graphs
arXiv:2606.08506v1 Announce Type: cross Abstract: Let $f(n,k)$ be the minimum size of a collection of bicliques such that (i) every edge of the complete graph $K_n$ is covered by at least one and at most $k$ bicliques in the collection, and (ii) for each edge $\{u,v\}$, the number of bicliques in which $u$ appears in the first class and $v$ in the second class differs by at most one from the number of bicliques in which $u$ appears in the second class and $v$ in the first class. For $k=1$,...
Tree Containment Parameterized by Scanwidth
arXiv:2605.31071v2 Announce Type: replace Abstract: TREE CONTAINMENT is a central decision problem in mathematical phylogenetics, asking whether a given rooted phylogenetic tree is embeddable in ("displayed by") a given rooted phylogenetic network. While the problem is NP-complete for general networks, many algorithmic advances have relied on structural parameters that capture how "tree-like" a network is. In this paper we investigate TREE CONTAINMENT under the structural parameter...
Tree Containment Parameterized by Scanwidth
Announce Type: new Abstract: TREE CONTAINMENT is a central decision problem in mathematical phylogenetics, asking whether a given rooted phylogenetic tree is embeddable in ("displayed by") a given rooted phylogenetic network. While the problem is NP-complete for general networks, many algorithmic advances have relied on structural parameters that capture how "tree-like" a network is. In this paper we investigate TREE CONTAINMENT under the structural parameter scanwidth, a directed width...
A 5.3-million-year-old deep-sea whale necropolis in the Diamantina Zone
Abstract Whale falls are biodiversity oases at seabeds1,2,3,4,5,6, yet their record from the oceans has remained sparse and fragmentary6,7. Here we report the discovery of a vast whale necropolis in the Diamantina Zone (4,616- to 7,001-m depth), extending about 1,200 km along the sea floor of the southeastern Indian Ocean. This area has a deep and extensive accumulation comprising five modern natural whale-fall communities and 476 fossil cetaceans recorded.