Daily edition · Algorithms
TILens turns technical updates into a focused daily brief: official releases, trusted reporting, and practitioner analysis, deduplicated and organized by topic.
arXiv:2608.17990v2 Announce Type: replace Abstract: The cluster graphs on $n$ vertices, the disjoint unions of complete graphs, have the integer partitions of $n$ as their isomorphism classes, and the quotient edit…
arXiv:2607.00612v2 Announce Type: replace Abstract: A non-empty string is closed if it has length one or its longest border appears exactly twice in the string. An occurrence of a closed substring is a maximal closed…
arXiv:2608.20924v1 Announce Type: new Abstract: Consider a set of bins and two-choice balls arriving by a Poisson process. We must allocate each incoming ball immediately to one of two incident bins. For a given…
arXiv:2507.19290v2 Announce Type: replace Abstract: We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-vector product (matvec)…
arXiv:2310.15152v3 Announce Type: replace-cross Abstract: We prove that a polynomial fraction of the set of $k$-component forests in the $m \times n$ grid graph have equal numbers of vertices in each component, for any…
arXiv:2608.21348v1 Announce Type: new Abstract: Calibration requires probabilistic reports to be conditionally unbiased and reliably interpretable as probabilities. A calibration measure assigns numerical error to…
arXiv:2602.05394v3 Announce Type: replace-cross Abstract: This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of…
arXiv:2608.20633v1 Announce Type: cross Abstract: The randomly pivoted Cholesky algorithm is one of the leading methods for computing a low-rank approximation to a large positive-semidefinite matrix. However, while it…
arXiv:2508.12536v4 Announce Type: replace-cross Abstract: Providing \textit{structured} information to large language models (LLMs) improves multi-step reasoning and factual grounding, and recent retrieval-augmented…
arXiv:2608.19149v2 Announce Type: replace Abstract: Suppose two parties, Alice and Bob, hold long character strings, $X$ and $Y$, respectively, and they are interested in determining how similar $X$ and $Y$ are.…
arXiv:2608.20559v1 Announce Type: new Abstract: We study the problem of estimating the number of hyperedges in an arbitrary $n$-vertex hypergraph using sublinear in $n$ queries. Note that the number of hyperedges, $m$,…
arXiv:2608.20894v1 Announce Type: cross Abstract: Planning accessible public services such as health care, emergency response, and schools often requires not only choosing where to open facilities but also improving the…
arXiv:2608.20437v1 Announce Type: new Abstract: An efficient $k$-limited dominating broadcast, or $k$-ELDB, is a $k$-limited broadcast in which every vertex is dominated exactly once. This notion brings together…
arXiv:2608.13782v2 Announce Type: replace-cross Abstract: The Johnson--Lindenstrauss lemma asserts that every set of $n$ points in $d$-dimensional Euclidean space embeds into $O(\varepsilon^{-2}\log n)$-dimensional…
arXiv:2608.07674v2 Announce Type: replace Abstract: In this paper, we study the {\em perfect fair-triangle packing} problem (abbreviated as PFTP), which incorporates the fairness criterion from {\em fair clustering}…
arXiv:2608.21248v1 Announce Type: cross Abstract: We study \emph{$T$-Robinson spaces}, a tree-based generalization of Robinson spaces in which every path of a compatible tree induces a Robinson subspace. This framework…
arXiv:2509.24309v4 Announce Type: replace Abstract: A forcing set $S$ in a combinatorial problem is a set of elements such that there is a unique solution that contains all the elements in $S$. An anti-forcing set is…
arXiv:2608.18577v2 Announce Type: replace Abstract: We study online service with one maximum-waiting-time charge per service batch. The persistent server endpoint prevents a phase-by-phase comparison with the offline…
arXiv:2608.20618v1 Announce Type: new Abstract: We study a stochastic multi-robot monitoring problem on a connected graph $G=(V,E)$, where each robot moves according to a Markov chain on $G$ and monitors the closed…
arXiv:2608.20767v1 Announce Type: new Abstract: Bipartite graphs are a fundamental representation for relational data arising in recommendation systems, social networks, and communication graphs. A key challenge in…
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