NP-解探索における質問計算量について

• 河内 亮周

  東京工業大学情報理工学研究科

• ロスマン ベンジャミン

  国立情報学研究所ビッグデータ数理国際研究センター

• 渡辺 治

  東京工業大学情報理工学研究科

書誌事項

タイトル別名

• Query Complexity of Witness Finding

抄録

In this paper we study a variant of search problems ? which we call witness finding problems ? in which there is no input and no underlying binary relation. Rather, there is a hidden set W from a fixed family W of possible sets. The objective is to output any element of W, where information about W is obtained by asking yes/no questions from a fixed family Q of permitted "queries". As the measure of complexity, we study the number of randomized queries required to find a witness in any nonempty W with high probability. By varying W and Q, this framework allows for some interesting upper and lower bounds. One classic upper bound for search problems ? which translates naturally into a witness finding algorithm ? is the search-to-decision reduction of Ben-David, Chor, Goldreich and Luby [3]. This algorithm solves the witness finding problem for arbitrary subsets of {0, 1}n using O(n2) non-adaptive queries from the family QNP of queries characterized by NP machines with an oracle to W. Our main result is a matching lower bound showing that Ω(n2) queries are necessary in this setting. We also present results and raise an intriguing question concerning the query complexity of witness finding with respect to affine witness sets and monotone queries.

収録刊行物

• 情報処理学会研究報告. AL, アルゴリズム研究会報告

  情報処理学会研究報告. AL, アルゴリズム研究会報告 2013 (7), 1-8, 2013-05-10

  一般社団法人情報処理学会

詳細情報

• CRID: 1574231877661006208
• NII論文ID: 110009579683
• NII書誌ID: AN1009593X
• ISSN: 09196072
• 本文言語コード: en
• データソース種別:
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