Tillmann Miltzow

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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)
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)
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)
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)
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)