{"paper":{"title":"A Box Decomposition Algorithm to Compute the Hypervolume Indicator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Carlos M. Fonseca, Kathrin Klamroth, Renaud Lacour","submitted_at":"2015-10-07T14:39:23Z","abstract_excerpt":"We propose a new approach to the computation of the hypervolume indicator, based on partitioning the dominated region into a set of axis-parallel hyperrectangles or boxes. We present a nonincremental algorithm and an incremental algorithm, which allows insertions of points, whose time complexities are $O(n^{\\lfloor \\frac{p-1}{2} \\rfloor+1})$ and $O(n^{\\lfloor \\frac{p}{2} \\rfloor+1})$, respectively. While the theoretical complexity of such a method is lower bounded by the complexity of the partition, which is, in the worst-case, larger than the best upper bound on the complexity of the hypervol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01963","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"}