By using a simple textbook reduction from vertex cover, we show that the following three problems are all UG-hard to approximate with constant-factor smaller than two; minimum weakness strong triadic closure, cluster deletion and constrained correlation clustering. Additionally, we analyze the well-known low-diameter decomposition by Calinescu, Karloff and Raban applied to the standard LP relaxation semi-metric for constrained correlation clustering. As opposed to traditional pivot-based approaches, a CKR partition elegantly handles must-link and cannot-link constraints. It guarantees a 3-approximation in expectation, which matches the original approximation ratio by van Zuylen and Williamson. We conjecture that it in fact achieves a strictly better than 3-approximation, yet this remains an open problem.
The paper develops an incidence-structural toolkit for this problem, and proves exact reductions for dominance, incidence twins, and weight-1 blocks; derive closed-form and low-weight upper bounds; introduce puncturing and covering certificates that sharpen those bounds; and analyze a layered greedy clustering algorith...
We analyze random constructions of independent sets in locally sparse graphs, specifically graphs with bounded maximum average degree in neighborhoods or with fractionally $r$-colorable neighborhoods. Specializing our methods to finding large independent sets and low-weight fractional colorings, we focus on optimizing...
For graph instances both for the min-max and the min-disagreement objectives, this work proves approximation guarantees that are substantially better than the bounds achievable for general graphs.
N. RajathRaoK, Jens Schlöter, Sami Davies et al.· 0 citations
We study pseudometric-weighted correlation clustering, where every pair of vertices carries a nonnegative disagreement weight and the weights satisfy the triangle inequality. For every fixed $\varepsilon>0$, we give a randomized polynomial-time $(2+\varepsilon)$-approximation, improving the previously best known factor...
This paper generalises the existing PTAS for complete graphs from a fixed to an arbitrary number of intervals and disprove an existing conjecture, which states that every instance of BIA admits a solution satisfying at least three quarters of all edges.
PeterBlohm, FlorianChen, A. Gionis et al.· 0 citations
Given a metric space graph
G
(
V, E
) in which only a subset of edge distances is known, we study a query-based model for answering lower bound distance queries on unknown edges, without access to any black-box distance oracle. For a queried pair of objects (
u, υ
) with unknown distance, the lower bound corres...
Swastika Biswas, Sohrab Namazi Nia, Jees Augustine et al.· Proceedings of the VLDB Endo...· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
