2026-07-24T11:53:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12921 2024-03-06T10:51:05Z ddc:004 open_access

Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral Flow Garg, Naveen Kumar, Nikhil Combinatorial Optimization Multicommodity Flow Network Design Given an edge weighted graph and a forest F, the 2-edge connectivity augmentation problem is to pick a minimum weighted set of edges, E', such that every connected component of E' ∪ F is 2-edge connected. Williamson et al. gave a 2-approximation algorithm (WGMV) for this problem using the primal-dual schema. We show that when edge weights are integral, the WGMV procedure can be modified to obtain a half-integral dual. The 2-edge connectivity augmentation problem has an interesting connection to routing flow in graphs where the union of supply and demand is planar. The half-integrality of the dual leads to a tight 2-approximate max-half-integral-flow min-multicut theorem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Naveen Garg and Nikhil Kumar 2020 Is Part Of LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2020.55 urn:nbn:de:0030-drops-129214 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.55 eng https://creativecommons.org/licenses/by/3.0/legalcode