{"paper":{"title":"The Bilinear Assignment Problem: Complexity and polynomially solvable special cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abraham P. Punnen, Ante \\'Custi\\'c, Binay Bhattacharya, Vladyslav Sokol","submitted_at":"2016-05-23T22:53:42Z","abstract_excerpt":"In this paper we study the {\\it bilinear assignment problem} (BAP) with size parameters $m$ and $n$, $m\\leq n$. BAP is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence NP-hard. We show that BAP cannot be approximated within a constant factor unless P=NP even if the associated quadratic cost matrix $Q$ is diagonal. Further, we show that BAP remains NP-hard if $m = O(\\sqrt[r]{n})$, for some fixed $r$, but is solvable in polynomial time if $m = O(\\sqrt{\\log n})$. When the rank of $Q$ is fixed, BAP is observed to admit FPTAS and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07234","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"}