Seminar Schedule のバックアップ(No.5)

数理工学特別セミナー / AMP PhD Seminar
2019年度秋学期 / Fall 2019 †

10月16日 / October 16 †

The first meeting of the semester.
Let us gather, greet new members to the Department, and set a plan for the semester before us.
We can play some warm-up board games to get to know each other, and hear some information on the ICT-Innovations event from experienced participants.

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10月21日 / October 21 †

Speaker: Shoya Motonaga
Dynamical Systems Group
Topic: TBA

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10月28日 / October 28 †

Speaker: Kaito Ito
Control Systems Theory Group
Topic: TBA

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11月6日 / November 6 †

Speaker: Naveed Ahmed Azam
Discrete Mathematics Group

Topic:
Counting Tree-Like Graphs with a Given Number of Vertices and Self-loops

Graph enumeration with given constraints is an interesting problem considered to be one of the fundamental problems in graph theory, with many applications in the natural sciences and engineering, such as bio-informatics and computational chemistry. For any two integers n ≥ 1 and ∆ ≥ 0, we propose a method to count all non-isomorphic trees with n vertices, ∆ self-loops, and no multi-edges, based on dynamic programming. To achieve this goal, we count the number of non-isomorphic rooted trees with n vertices, ∆ self-loops and no multi-edges, in O(n^2(n + ∆(n + ∆ · min{n, ∆}))) time and O(n^2(∆^2 + 1)) space, since every tree can be uniquely viewed as a rooted tree by either regarding its unicentroid as the root, or in the case of bicentroid, by introducing a virtual vertex on the bicentriod and assuming the virtual vertex to be the root.

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