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- Tillmann Miltzow
- FUN
- 2012

We study the combinatorial two-player game Tron. We answer the extremal question on general graphs and also consider smaller graph classes. Bodlaender and Kloks conjectured in [2] PSPACE-completeness. We proof this conjecture.

- Andrei Asinowski, Balázs Keszegh, Tillmann Miltzow
- Discrete Mathematics
- 2014

In an instance of the house allocation problem, two sets A and B are given. The set A is referred to as applicants and the set B is referred to as houses. We denote by m and n the size of A and B respectively. In the house allocation problem, we assume that every applicant a ∈ A has a preference list over the set of houses B. We call an injective mapping τ… (More)

- Oswin Aichholzer, Tillmann Miltzow, Alexander Pilz
- Comput. Geom.
- 2013

- Édouard Bonnet, Tillmann Miltzow
- ESA
- 2016

Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S. The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P.… (More)

- Oswin Aichholzer, Andrei Asinowski, Tillmann Miltzow
- Electr. J. Comb.
- 2015

Let X 2k be a set of 2k labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of X 2k. Two such matchings, M and M , are disjoint compatible if they do not have common edges, and no edge of M crosses an edge of M. Denote by DCM k the graph whose vertices correspond to such matchings, and two… (More)

- Édouard Bonnet, Tillmann Miltzow
- Symposium on Computational Geometry
- 2017

Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S. The set S is referred to as guards. Assuming integer coordinates and a specific general… (More)

We consider several classes of intersection graphs of line segments in the plane and prove new equality and separation results between those classes. In particular, we show that: • intersection graphs of grounded segments and intersection graphs of downward rays form the same graph class, • not every intersection graph of rays is an intersection graph of… (More)

- Édouard Bonnet, Tillmann Miltzow, Pawel Rzazewski
- STACS
- 2017

In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is… (More)

- Andrei Asinowski, Tillmann Miltzow, Günter Rote
- JoCG
- 2015

Given n red and n blue points in general position in the plane, it is well-known that there is a perfect matching formed by non-crossing line segments. We characterize the bichromatic point sets which admit exactly one non-crossing matching. We give several geometric descriptions of such sets, and find an O(n log n) algorithm that checks whether a given… (More)