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Probabilistic AVL Trees (p-AVL): Relaxing Deterministic Balancing
arXiv:2604.02223v1 Announce Type: new Abstract: This paper studies the empirical behaviour of the p-AVL tree, a probabilistic variant of the AVL tree in which each imbalance is repaired with probability $p$. This gives an exact continuous interpolation from $p = 0$, which recovers the BST endpoint, to $p = 1$, which recovers the standard AVL tree. Across random-order insertion experiments, we track rotations per node, total imbalance events, average depth, average height, and a global imbalance statistic $\sigma$. The main empirical result is that even small nonzero p already causes a strong structural change. The goal here is empirical rather than fully theoretical: to document the behaviour of the p-AVL family clearly and identify the main patterns.
Adaptive Fully Dynamic $k$-Center Clustering with (Near-)Optimal Worst-Case Guarantees
arXiv:2604.01726v1 Announce Type: new Abstract: Given a sequence of adversarial point insertions and point deletions, is it possible to simultaneously optimize the approximation ratio, update time, and recourse for a $k$-clustering problem? If so, can this be achieved with worst-case guarantees against an adaptive adversary? These questions have garnered significant attention in recent years. Prior works by Bhattacharya, Costa, Garg, Lattanzi, and Parotsidis [FOCS '24] and by Bhattacharya, Costa, and Farokhnejad [STOC '25] have taken significant steps toward this direction for the $k$-median clustering problem and its generalization, the $(k, z)$-clustering problem. In this paper, we study the $k$-center clustering problem, which is one of the most classical and well-studied $k$-clustering
DGAI: Decoupled On-Disk Graph-Based ANN Index for Efficient Updates and Queries
arXiv:2510.25401v3 Announce Type: replace Abstract: On-disk graph-based indexes are favored for billion-scale Approximate Nearest Neighbor Search (ANNS) due to their high performance and cost-efficiency. However, existing systems typically rely on a coupled storage architecture that co-locates vectors and graph topology, which introduces substantial redundant I/O during index updates, thereby degrading usability in dynamic workloads. In this paper, we propose a decoupled storage architecture that physically separates heavy vectors from the lightweight graph topology. This design substantially improves update performance by reducing redundant I/O during updates. However, it introduces I/O amplification during ANNS, leading to degraded query efficiency.To improve query performance within the
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More in Research Papers
Probabilistic AVL Trees (p-AVL): Relaxing Deterministic Balancing
arXiv:2604.02223v1 Announce Type: new Abstract: This paper studies the empirical behaviour of the p-AVL tree, a probabilistic variant of the AVL tree in which each imbalance is repaired with probability $p$. This gives an exact continuous interpolation from $p = 0$, which recovers the BST endpoint, to $p = 1$, which recovers the standard AVL tree. Across random-order insertion experiments, we track rotations per node, total imbalance events, average depth, average height, and a global imbalance statistic $\sigma$. The main empirical result is that even small nonzero p already causes a strong structural change. The goal here is empirical rather than fully theoretical: to document the behaviour of the p-AVL family clearly and identify the main patterns.
A Constant-Approximation Distance Labeling Scheme under Polynomially Many Edge Failures
arXiv:2604.01829v1 Announce Type: new Abstract: A fault-tolerant distance labeling scheme assigns a label to each vertex and edge of an undirected weighted graph $G$ with $n$ vertices so that, for any edge set $F$ of size $|F| \leq f$, one can approximate the distance between $p$ and $q$ in $G \setminus F$ by reading only the labels of $F \cup \{p,q\}$. For any $k$, we present a deterministic polynomial-time scheme with $O(k^{4})$ approximation and $\tilde{O}(f^{4}n^{1/k})$ label size. This is the first scheme to achieve a constant approximation while handling any number of edge faults $f$, resolving the open problem posed by Dory and Parter [DP21]. All previous schemes provided only a linear-in-$f$ approximation [DP21, LPS25]. Our labeling scheme directly improves the state of the art in
Adaptive Fully Dynamic $k$-Center Clustering with (Near-)Optimal Worst-Case Guarantees
arXiv:2604.01726v1 Announce Type: new Abstract: Given a sequence of adversarial point insertions and point deletions, is it possible to simultaneously optimize the approximation ratio, update time, and recourse for a $k$-clustering problem? If so, can this be achieved with worst-case guarantees against an adaptive adversary? These questions have garnered significant attention in recent years. Prior works by Bhattacharya, Costa, Garg, Lattanzi, and Parotsidis [FOCS '24] and by Bhattacharya, Costa, and Farokhnejad [STOC '25] have taken significant steps toward this direction for the $k$-median clustering problem and its generalization, the $(k, z)$-clustering problem. In this paper, we study the $k$-center clustering problem, which is one of the most classical and well-studied $k$-clustering
Single-Pass Streaming CSPs via Two-Tier Sampling
arXiv:2604.01575v1 Announce Type: new Abstract: We study the maximum constraint satisfaction problem, Max-CSP, in the streaming setting. Given $n$ variables, the constraints arrive sequentially in an arbitrary order, with each constraint involving only a small subset of the variables. The objective is to approximate the maximum fraction of constraints that can be satisfied by an optimal assignment in a single pass. The problem admits a trivial near-optimal solution with $O(n)$ space, so the major open problem in the literature has been the best approximation achievable when limiting the space to $o(n)$. The answer to the question above depends heavily on the CSP instance at hand. The integrality gap $\alpha$ of an LP relaxation, known as the BasicLP, plays a central role. In particular, a
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