[
    {
        "id": "thesis:18812",
        "collection": "thesis",
        "collection_id": "18812",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06092026-171629445",
        "primary_object_url": {
            "basename": "senior thesis.pdf",
            "content": "final",
            "filesize": 311585,
            "license": "other",
            "mime_type": "application/pdf",
            "url": "/18812/1/senior thesis.pdf",
            "version": "v3.0.0"
        },
        "type": "thesis",
        "title": "Worst-Case to Average-Case Reductions for Matrix\r\nMultiplication via Additive Combinatorics",
        "author": [
            {
                "family_name": "McNichols",
                "given_name": "Nia M.",
                "orcid": "0000-0002-5132-9661",
                "clpid": "McNichols-Nia-M"
            }
        ],
        "thesis_advisor": [
            {
                "family_name": "Umans",
                "given_name": "Christopher M.",
                "orcid": "0000-0002-6390-9401",
                "clpid": "Umans-C-M"
            }
        ],
        "thesis_committee": [
            {
                "family_name": "None",
                "given_name": "None"
            }
        ],
        "local_group": [
            {
                "literal": "div_eng"
            }
        ],
        "abstract": "In the field of average-case complexity, we are concerned with how an algorithm performs on an average input, rather than the classical worst-case analysis. Of particular interest are worst-case to average-case reductions, that is transforming an algorithm that works on some fraction of inputs into a probabilistic one that works on <em>all</em> inputs. Building on recent results in the field, we present a framework for average-case matrix multiplication algorithms. Explicitly, our framework provides a transformation for algorithms running in time T(n) that work on a small fraction of inputs into ones running in time &#213;(T(n)) that work on all inputs, even in the case when this fraction rapidly tends to 0. Moreover, our framework requires fewer non-trivial results than similar methods, at the cost of minor asymptotic losses.",
        "doi": "10.7907/4xz0-v816",
        "publication_date": "2023",
        "thesis_type": "senior_major",
        "thesis_year": "2023"
    }
]