Special cases of routing problems and their crossings

• Project/Area Number: 21740082
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Keio University
• Principal Investigator: ODA Yoshiaki 慶應義塾大学, 理工学部, 准教授 (90325043)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 離散数学 / 組合せ論 / 巡回セールスマン問題 / アルゴリズム / 計算量理論

Research Abstract

The Traveling Salesman Problem is one of the most famous NP-hard problems. In this work, we studied polynomial time solvable cases for the problem and its extended problems ; the Vehicle Routing Problem and the Multi-Depot VRP. Especially, we focused on "crossings" for those cases. Also, we studied a problem to obtain a non-crossing Hamiltonian cycle by repeating "flip" operations and analogous problems.

Research Products

• [Journal Article] K_6-minors in triangulations on the nonorientable surface of genus 3 (2010)
  • Author(s): R. Mukae, A. Nakamoto, Y. Oda, Y. Suzuki
  • Journal Title: Graphs and Combinatorics Volume: 26 Pages: 559-570
  • Peer Reviewed
• [Journal Article] 3-trees with few vertices of degree 3 in circuit graphs (2009)
  • Author(s): A. Nakamoto, Y. Oda and K. Ota
  • Journal Title: Discrete Mathematics Volume: 309 Pages: 666-672
  • Peer Reviewed
• [Presentation] 反転に関するいくつかの問題 (2012)
  • Author(s): 小田芳彰
  • Organizer: 関西グラフ理論研究集会
  • Place of Presentation: 加計国際学術交流センタ
  • Year and Date: 2012-03-07
• [Presentation] 反転に関するいくつかの問題 (2012)
  • Author(s): 小田芳彰
  • Organizer: 関西グラフ理論研究集会
  • Place of Presentation: 加計国際学術交流センター
  • Year and Date: 2012-03-07
• [Presentation] 経路問題と計算量-経路問題の多項式時間で解けるクラス (2011)
  • Author(s): 小田芳彰
  • Organizer: 離散数理構造とその応用
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2011-11-19
• [Presentation] 経路問題と計算量-経路問題の多項式時間で解けるクラス (2011)
  • Author(s): 小田芳彰
  • Organizer: 研究集会「離散数理構造とその応用」
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2011-11-19
• [Presentation] 複数の倉庫がある車両配送問題の多項式時間で解けるクラス (2010)
  • Author(s): 小田芳彰
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2010-12-18
• [Presentation] Special cases of the multi-depot vehicle routing problem (2010)
  • Author(s): Yoshiaki Oda
  • Organizer: The 3^<rd> Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Tokai University Pacific Center, Hawaii
  • Year and Date: 2010-12-09
• [Presentation] 経路問題と離散数学 (2009)
  • Author(s): 小田芳彰
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] 経路問題と離散数学 (2009)
  • Author(s): 小田芳彰
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Remarks]