Finding a Maximum 2-Matching Excluding Prescribed Cycles in Bipartite Graphs

We introduce a new framework of restricted 2-matchings close to Hamilton cycles. For an undirected graph (V,E) and a family U of vertex subsets, a 2-matching F is called U-feasible if, for each setU in U, F contains at most |setU|-1 edges in the subgraph induced by U. Our framework includes C_{= 5. For instance, in bipartite graphs in which every cycle of length six has at least two chords, our algorithm solves the maximum C_{<=6}-free 2-matching problem in O(n^2 m) time, where n and m are the numbers of vertices and edges, respectively

Matching, matroid, and traveling salesman problem

研究成果の概要 (和文) : 巡回セールスマン問題 (TSP) は，おそらくもっとも有名な NP 困難な問題であり，TSPに対して提案された数々の手法は，離散最適化の分野全体の発展に大いに寄与してきた．特に近年，TSPに対する理論的なブレイクスルーといえる研究が数多く発表されている．本研究は，TSPへの応用を念頭に置き，離散最適化問題の効率的な解法の基礎をなす理論であるマッチング理論およびマトロイド理論の深化と拡大を行った．本研究で発表した 20篇の論文はすべて，最適化分野のトップジャーナル・トップカンファレンスを含む，定評のある査読付き国際論文誌に採録，または査読付き国際会議に採択されている．研究成果の概要 (英文) : The traveling salesman problem (TSP) is perhaps the most famous NP-hard problem, and has enhanced developments of many methods in the field of discrete optimization. In particular, TSP attracts recent intensive attention: several theoretical breakthrough papers have been published in this past decade.Our research has intended to be applied in theoretical improvement in solving TSP. Specifically, our research has achieved deepening and extending of matching theory and matroid theory, which form bases of efficient solutions to discrete optimization problems. All of our 20 papers has been accepted to reputable, international, peer-reviewed journals or conferences, including top journals and conferences in the field of optimization