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DTSTART:20220101T000000
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DTSTART;TZID=Asia/Seoul:20230103T163000
DTEND;TZID=Asia/Seoul:20230103T173000
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CREATED:20221010T054006Z
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SUMMARY:Youngho Yoo (유영호)\, Approximating TSP walks in subcubic graphs
DESCRIPTION:The Graphic Travelling Salesman Problem is the problem of finding a spanning closed walk (a TSP walk) of minimum length in a given connected graph. The special case of the Graphic TSP on subcubic graphs has been studied extensively due to their worst-case behaviour in the famous $\frac{4}{3}$-integrality-gap conjecture on the “subtour elimination” linear programming relaxation of the Metric TSP. \nWe prove that every simple 2-connected subcubic graph on $n$ vertices with $n_2$ vertices of degree 2 has a TSP walk of length at most $\frac{5n+n_2}{4}-1$\, confirming a conjecture of Dvořák\, Král’\, and Mohar. This bound is best possible and we characterize the extremal subcubic examples meeting this bound. We also give a quadratic time combinatorial algorithm to find such a TSP walk. In particular\, we obtain a $\frac{5}{4}$-approximation algorithm for the Graphic TSP on cubic graphs. Joint work with Michael Wigal and Xingxing Yu.
URL:https://dimag.ibs.re.kr/event/2023-01-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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