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String Representation in Suffixient Set Size Space

arXiv:2604.04377v1 Announce Type: new Abstract: Repetitiveness measures quantify how much repetitive structure a string contains and serve as parameters for compressed representations and indexing data structures. We study the measure $\chi$, defined as the size of the smallest suffixient set. Although $\chi$ has been studied extensively, its reachability, whether every string $w$ admits a string representation of size $O(\chi(w))$ words, has remained an important open problem. We answer this question affirmatively by presenting the first such representation scheme. Our construction is based on a new model, the substring equation system (SES), and we show that every string admits an SES of size $O(\chi(w))$.

arXiv cs.DS

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Causality-Based Scores Alignment in Explainable Data Management

arXiv:2503.14469v5 Announce Type: replace Abstract: Different attribution scores have been proposed to quantify the relevance of database tuples for query answering in databases; e.g. Causal Responsibility, the Shapley Value, the Banzhaf Power-Index, and the Causal Effect. They have been analyzed in isolation. This work is a first investigation of score alignment depending on the query and the database; i.e. on whether they induce compatible rankings of tuples. We concentrate mostly on causality-based scores; and provide a syntactic dichotomy result for queries: on one side, pairs of scores are always aligned, on the other, they are not always aligned. It turns out that the presence of exogenous tuples makes a crucial difference in this regard.

arXiv cs.DB

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Improved Upper Bounds for the Directed Flow-Cut Gap

arXiv:2604.03412v1 Announce Type: new Abstract: We prove that the flow-cut gap for $n$-node directed graphs is at most $n^{1/3 + o(1)}$. This is the first improvement since a previous upper bound of $\widetilde{O}(n^{11/23})$ by Agarwal, Alon, and Charikar (STOC '07), and it narrows the gap to the current lower bound of $\widetilde{\Omega}(n^{1/7})$ by Chuzhoy and Khanna (JACM '09). We also show an upper bound on the directed flow-cut gap of $W^{1/2}n^{o(1)}$, where $W$ is the sum of the minimum fractional cut weights. As an auxiliary contribution, we significantly expand the network of reductions among various versions of the directed flow-cut gap problem. In particular, we prove near-equivalence between the edge and vertex directed flow-cut gaps, and we show that when parametrizing by $W

arXiv cs.DS

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Cardinality Estimation for High Dimensional Similarity Queries with Adaptive Bucket Probing

arXiv:2604.04603v1 Announce Type: new Abstract: In this work, we address the problem of cardinality estimation for similarity search in high-dimensional spaces. Our goal is to design a framework that is lightweight, easy to construct, and capable of providing accurate estimates with satisfying online efficiency. We leverage locality-sensitive hashing (LSH) to partition the vector space while preserving distance proximity. Building on this, we adopt the principles of classical multi-probe LSH to adaptively explore neighboring buckets, accounting for distance thresholds of varying magnitudes. To improve online efficiency, we employ progressive sampling to reduce the number of distance computations and utilize asymmetric distance computation in product quantization to accelerate distance calc

arXiv cs.DB

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