{"paper":{"title":"The Shape of the Search Tree for the Maximum Clique Problem, and the Implications for Parallel Branch and Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Ciaran McCreesh, Patrick Prosser","submitted_at":"2014-01-23T10:01:35Z","abstract_excerpt":"Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel explanation as to why they are successful. We show that load balance is sometimes a problem, but that the interaction of parallel search order and the most likely location of solutions within the search space is often the dominating consideration. We use this explanation to propose a new low-overhead, scalable work splitting mechanism. Our approach uses exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5921","kind":"arxiv","version":3},"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"}