Computer Science > Data Structures and Algorithms
arXiv:2503.00712 (cs)
[Submitted on 2 Mar 2025 (v1), last revised 15 Apr 2025 (this version, v2)]
Title:Streaming Algorithms for Network Design
View a PDF of the paper titled Streaming Algorithms for Network Design, by Chandra Chekuri and 3 other authors
View PDFHTML (experimental)Abstract:We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph $G = (V, E)$ and an integer connectivity requirement $r(uv)$ for each $u, v \in V$. The objective is to find a min-weight subgraph $H \subseteq G$ s.t., for every pair of $u, v \in V$, $u$ and $v$ are $r(uv)$-edge/vertex-connected. Recent work by Jin et al. [JKMV24] obtained approximation algorithms for edge-connectivity augmentation, and via that, also derived algorithms for edge-connectivity SNDP (EC-SNDP). We consider vertex-connectivity setting (VC-SNDP) and obtain several results for it as well as improved results for EC-SNDP.
* We provide a general framework for solving connectivity problems in streaming; this is based on a connection to fault-tolerant spanners. For VC-SNDP, we provide an $O(tk)$-approximation in $\tilde O(k^{1-1/t}n^{1 + 1/t})$ space, where $k$ is the maximum connectivity requirement, assuming an exact algorithm at the end of the stream. Using a refined LP-based analysis, we provide an $O(\beta t)$-approximation where $\beta$ is the integrality gap of the natural cut-based LP relaxation. When applied to the EC-SNDP, our framework provides an $O(t)$-approximation in $\tilde O(k^{1/2-1/(2t)}n^{1 + 1/t} + kn)$ space, improving the $O(t \log k)$-approximation of [JKMV24] using $\tilde O(kn^{1+1/t})$ space; this also extends to element-connectivity SNDP.
* We consider vertex connectivity-augmentation in the link-arrival model. The input is a $k$-vertex-connected subgraph $G$, and the weighted links $L$ arrive in the stream; the goal is to store the min-weight set of links s.t. $G \cup L$ is $(k+1)$-vertex-connected. We obtain $O(1)$ approximations in near-linear space for $k = 1, 2$. Our result for $k=2$ is based on SPQR tree, a novel application for this well-known representation of $2$-connected graphs.
| Subjects: | Data Structures and Algorithms (cs.DS) |
| Cite as: | arXiv:2503.00712 [cs.DS] |
| (orarXiv:2503.00712v2 [cs.DS] for this version) | |
| https://doi.org/10.48550/arXiv.2503.00712 arXiv-issued DOI via DataCite |
Submission history
From: Ali Vakilian [view email][v1] Sun, 2 Mar 2025 03:35:47 UTC (102 KB)
[v2] Tue, 15 Apr 2025 19:53:41 UTC (105 KB)
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View a PDF of the paper titled Streaming Algorithms for Network Design, by Chandra Chekuri and 3 other authors
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