{"id":1151900,"date":"2025-10-14T11:42:39","date_gmt":"2025-10-14T18:42:39","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=1151900"},"modified":"2025-10-14T11:42:40","modified_gmt":"2025-10-14T18:42:40","slug":"streaming-algorithms-for-network-design","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/streaming-algorithms-for-network-design\/","title":{"rendered":"Streaming Algorithms for Network Design"},"content":{"rendered":"<p>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\u00a0 r(u,v) for each u,v\u2208V. The objective is to find a min-weight subgraph H\u2286G s.t., for every pair of u,v\u2208V,u\u00a0 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.<\/p>\n<ul>\n<li>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 \u00d5(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(\u03b2t)-approximation where \u03b2 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 \u00d5(k^{1\/2 &#8211; 1\/(2t)} n^{1+1\/t}+kn) space, improving the O(t log k)-approximation of [JKMV24] using \u00d5(k n^{1+1\/t}) space; this also extends to element-connectivity SNDP.<\/li>\n<li>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\u222aL 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.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>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\u00a0 r(u,v) for each u,v\u2208V. The objective is to find a min-weight subgraph H\u2286G s.t., for every pair of u,v\u2208V,u\u00a0 and v are r(uv)-edge\/vertex-connected. Recent work by Jin [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"International Conference on Approximation Algorithms for Combinatorial Optimization Problems 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