Mittagsseminar (by J. Lengler, K. Bringmann, B. Gärtner, M. Hoffmann, R. Kyng, D.Steurer, V. Traub)

Date and Time: Tuesday, June 16, 2026, 12:15 pm

Duration: 30 minutes

Location: OAT S15

Speaker: Yanheng Wang

Touring a Sequence of Orthogonal Polygons

Consider a sequence of polygons P_1, ..., P_k with a total of n vertices. Our goal is to find a point p_i in P_i for each i, such that dist(p_1, p_2) + ... + dist(p_{k-1}, p_k) is minimized.

My talk focuses on the Manhattan distance. The problem is NP-hard in general. I will present an O(n^{1.98}) algorithm when the polygons are rectilinear and disjoint. This breaks the quadratic barrier of the naive dynamic programming approach. To achieve this, we partition the timeline [k] and the space R^2 in a way that the subproblems can be handled efficiently by (less straightforward) dynamic programming and planar distance oracles, and that we can link the subproblems together efficiently.

This is joint work with Katrin Casel, Sándor Kisfaludi-Bak, Linda Kleist, Jeroen S.K. Lamme, and Eunjin Oh.

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