This thesis considers a variant of the classical problem for finding the longest common subsequence (LCS) called longest common subsequence problem with a gapped constraint (LCSGC). Given two sequences A, B, and a constrained sequence C, which is accomplished with a corresponding gapped constraint for each symbol, whose lengths are m, n, and r, respectively, the LCSGC problem is to find an LCS of A and B, such that C is also a subsequence of this LCS and the gapped constraints corresponding to C are satisfied. In this thesis, two algorithms with time complexities O(m2n2r) and O(mnr ¡Ñ min(m, n)) are proposed based on the dynamic programming technique for solving the LCSGC problem.

2001年5月29日第11次《聯合國海洋法公約》締約國會議通過SPLOS/72號決定，於1999年5月13日以前對其生效之公約締約國，如欲依《聯合國海洋法公約》第76條規定主張200海里以外之大陸礁層，必須在1999年5月13日起算10年內向聯合國大陸礁層界限委員會提交與其所主張大陸礁層外部界限相關科學及技術佐證資料。由於《聯合國海洋法公約》所定義之大陸礁層外部界限範圍可能超越專屬經濟海域範圍，而大陸礁層不僅是魚類資源較豐富也是漁業活動重要資源地，同時也是海底油氣與礦場等重要自然資源的集中地區。因此，包括我國相鄰之日本、菲律賓、越南、馬來西亞等公約締約國紛紛進行大陸礁層調查來擴展自己國家的海洋權益。至2009年12月止，已有51個延伸大陸礁層外部界限之提案，及44個初步資訊，聯合國大陸礁層界限委員會並已就部分提案作成決議。 日本於2008年11月12日向聯合國大陸礁層界限委員會提出該國延伸大陸礁層外部界限之申請，卻也因此引起中國大陸及韓國對日本提案中以「沖之鳥礁」為基礎劃定超出200海里延伸大陸礁層之主張提出反對意見，質疑「沖之鳥礁」之法律地位及其所能享有的海域管轄空間。本論文爰由《聯合國海洋法公約》第121條「島嶼制度」形成的過程、相關國家實踐及學者見解，以及《聯合國海洋法公約》中「大陸礁層」之相關規範及聯合國大陸礁層界限委員會之組織與運作情形，探討日本的延伸大陸礁層外部界限提案中以「沖之鳥礁」為基礎主張延伸大陸礁層之適法性問題，並分析以聯合國大陸礁層界限委員會作為「沖之鳥礁」法律地位爭端解決途徑之可能性等。研究結果顯示，日本提案以「沖之鳥礁」為基礎主張延伸大陸礁層外部界限不符合《聯合國海洋法公約》第121條第3項規定，但該項規定並未具備有習慣國際法的效力，亦缺乏客觀的認定標準，聯合國大陸礁層界限委員會的場域無法解決「沖之鳥礁」的法律地位爭端，其他沿海國僅能利用聯合國大陸礁層界限委員會中「第三國意見」之機制凸顯爭端的存在，提醒國際社會注意此類島礁的海域管轄空間主張的合理性問題，並應尊重公約所賦予的權利與義務。 / On 29 May 2001, the 11th Meeting of States Parties to the United Nations Convention on the Law of the Sea (UNCLOS) adopted the SPLOS/72 Decision regarding the date of commencement of the ten-year period for making submissions to the Commission on the Limits of the Continental Shelf set out in Article 4 of Annex II to the UNCLOS. It was decided that, in the case of a State Party for which the Convention entered into force before 13 May 1999, the ten-year time period for it to submit the scientific and technical data supporting the outer limits of its continental shelf beyond 200 nautical miles under Article 76 of the UNCLOS shall be taken to have commenced on 13 May 1999. For quite a few States the outer limits of their continental shelf as defined by the UNCLOS may go beyond the limits of the Exclusive Economic Zone (EEZ). Besides, continental shelf is abundant in fisheries resources, crude oil, natural gas and minerals. Consequently, the neighboring States of Taiwan, including Japan, the Philippines, Viet Nam, and Malaysia, have already begun their surveys on continental shelf in order to expand their interests hidden in the ocean. As of December of 2009, there have been 51 formal submissions and 44 Preliminary Information delivered to the United Nations. The Commission on the Limits of the Continental Shelf (CLCS) has been undertaking the consideration of these submissions and already completed such process for some of them with recommendations. For Japan, the submission to support the outer limits of its extended continental shelf was made on 12 November 2008 to the CLCS. Such submission was challenged by China and Korea whose focus is on the part of extended continental shelf generated by Oki-no-tori Shima. The legal status of Oki-no-tori Shima as being capable of generating EEZ, continental shelf, and extended continental shelf beyond 200 nautical miles, is being disputed by the communications from China and Korea. To provide educated comments on such controversy, this thesis will discuss the legislative process of Article 121 of the UNCLOS, namely, the regime of islands. Related state practices and teachings of the most highly qualified publicists will be studied in this connection. The author will also examine the regime of continental shelf under the UNCLOS and the institution of the CLCS. These will pave the way to scrutinize the legality of using Oki-no-tori Shima as the basis to generate extended continental shelf as having been done by Japan in its submission. The author will also explore the feasibility for the CLCS to settle the dispute over the legality of Japanese submission with respect to Oki-no-tori Shima. As shown by research works, the Japanese submission using Oki-no-tori Shima to generate extended continental shelf is inconsistent with Article 121(3) of the UNCLOS. However, the rule as contained in Article 121(3) has not yet been received into customary international law. Also lacking are the objective criteria to decide whether a given rock meets the conditions as stipulated by Article 121(3) or not. The forum of the CLCS is not suitable to settle the dispute over the legality of using Oki-no-tori Shima by Japan to generate extended continental shelf. Other coastal States can only use the forum of the CLCS to demonstrate the legal controversy over this case through sending third party communications to notify the CLCS the existence of dispute and their unwillingness to support the CLCS to consider the Japanese submission with respect to the part of Oki-no-tori Shima. As submitted by this author, the international community should be reminded of the necessity to respect the integrity of the rights and duties enshrined by the UNCLOS. Also worthy of careful scrutiny is the legitimacy of such kinds of exaggerated maritime claims generated by the rock as defined by Article 121(3) of the UNCLOS.