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Can Neural Networks Achieve Optimal Computational-statistical Tradeoff? An Analysis on Single-Index Model Differentially Private Submodular Maximization with a Knapsack Constraint Linear algebra at exponential scale via tensor network dimension reduction Optimality of Random Regular Graphs in Sparse Network Designs Modern Primal-Dual Frameworks for Prior-Free Online Resource Allocation Comparison Patrols on Drifting Orders: Certified Rank Maintenance, Evolving Planar Maxima, and Selection under Drifting Fitness Threshold Minimum Cut with Terminal Quotas: Logarithmic and Planar Approximation Algorithms Distributed Dominating Set With Optimal Rounds and Message Size in Bounded Arboricity Graphs Active Learning with Low-Rank Structure for Data Selection Raiders of the Lost Log: Synchronous Parallel In-Place Models and Algorithms C^2: Cache-Conscious Succinct Tries with Adaptive Unary Path Compression Resizable Retrieval Contested Cluster Selectors: Local Ambiguity, Normal Forms, and Backtracking Cost in Random Constraint Satisfaction Single-item lot sizing problem under budgeted lead-time uncertainty Online Matching with KIID Edge Arrivals Coresets for Continuous $k$-Center in Hyperbolic Space A constant-factor approximation of the Gromov-Hausdorff distance in the plane Recoverable robust shortest path problem under interval budgeted uncertainty representations Complexity Classes for Online Problems with and without Predictions Improved Certificates for Independence Number in Semirandom Hypergraphs Computational Generation of Substrate-Specific Molecular Cages Faster Linear-Space Data Structures for Path Frequency Queries Improved Parallel Algorithms for EF1 Allocations Lower bounds for the universal TSP on the plane Optimal learning of quantum channels in diamond distance Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing Characterizations of Admissible Objective Functions for Hierarchical Clustering
Problems related to strong connectivity and strong biconnectivity
[Submitted on 15 Jun 2026] · 2026-06-16 · via cs.DS updates on arXiv.org

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Abstract:Let $G=(V,E)$ be a strong biconnected graph and let $B \subseteq V$ such that for each vertex $w \in B$, the subgraph $G \setminus \lbrace w\rbrace$ is strongly connected. In this paper we study the problem of computing a subset $E_{\beta} \subseteq E$ of minimum size such that the subgraph $G_{\beta}=(V,E_{\beta})$ is strongly biconnected and for each vertex $w \in B$, the subgraph $G_{\beta} \setminus \lbrace w\rbrace$ is strongly connected. We prove that there exists a polynomial time $7$-approximation algorithm for this problem.

Submission history

From: R Jaberi [view email]
[v1] Mon, 15 Jun 2026 00:56:38 UTC (10 KB)