{"paper":{"title":"Approximating Minimum Dominating Set on String Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DM","authors_text":"Dibyayan Chakraborty, Joydeep Mukherjee, Sandip Das","submitted_at":"2018-09-26T13:38:56Z","abstract_excerpt":"In this paper, we give approximation algorithms for the \\textsc{Minimum Dominating Set (MDS)} problem on \\emph{string} graphs and its subclasses. A \\emph{path} is a simple curve made up of alternating horizontal and vertical line segments. A \\emph{$k$-bend path} is a path made up of at most $k + 1$ line segments. An \\textsc{L}-path is a $1$-bend path having the shape `\\textsc{L}'. A \\emph{vertically-stabbed-\\textsc{L} graph} is an intersection graph of \\textsc{L}-paths intersecting a common vertical line. We give a polynomial time $8$-approximation algorithm for \\textsc{MDS} problem on vertica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09990","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}