{"paper":{"title":"Approximation algorithms and an integer program for multi-level graph spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Faryad Darabi Sahneh, Keaton Hamm, Mohammad Javad Latifi Jebelli, Reyan Ahmed, Richard Spence, Stephen Kobourov","submitted_at":"2019-04-01T22:48:08Z","abstract_excerpt":"Given a weighted graph $G(V,E)$ and $t \\ge 1$, a subgraph $H$ is a \\emph{$t$--spanner} of $G$ if the lengths of shortest paths in $G$ are preserved in $H$ up to a multiplicative factor of $t$. The \\emph{subsetwise spanner} problem aims to preserve distances in $G$ for only a subset of the vertices. We generalize the minimum-cost subsetwise spanner problem to one where vertices appear on multiple levels, which we call the \\emph{multi-level graph spanner} (MLGS) problem, and describe two simple heuristics. Applications of this problem include road/network building and multi-level graph visualiza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01135","kind":"arxiv","version":1},"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"}