Tillmann Miltzow

Complexity of token swapping and its variants

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

Extreme point and halving edge search in abstract order types

W[1]

Tron, a combinatorial game on abstract graphs

-hard parameterized by the length

Parameterized Hardness of Art Gallery Problems

k

Intersection Graphs of Rays and Grounded Segments

of a shortest sequence of swaps. In fact, we prove that, for any computable function

Approximation and Hardness of Token Swapping

f

Irrational Guards are Sometimes Needed.

, it cannot be solved in time

An Approximation Algorithm for the Art Gallery Problem

f(k)n^{o(k / \log k)}

Halving Balls in Deterministic Linear Time

where

Counting Houses of Pareto Optimal Matchings in the House Allocation Problem

n