arXiv subjects

Mia Müßig

Publications and source records attributed to Mia Müßig.

4 recordsLinked to original sources

arXiv2026

Maximum independent queen set on polyominoes is NP-complete

Finding a set of vertices in a graph with no edges between them, INDSET, is a well-known NP-complete problem. The queen graph of a chessboard is constructed by taking vertices as the tiles of the chessboard and drawing edges between two tiles if a queen can move from one to the other. We call INDQUEENS the independent set problem on a queen graph where the chessboard is a polyomino. We prove that INDQUEENS on polyominoes is NP-complete, proving a conjecture of Langlois-Rémillard--Müßig--Roldán. As our reduction is parsimonious, we can further prove that it is #P-complete. We furthermore prove that INDROOKS on polyominoes is #P-complete, despite being solvable in polynomial time.

cs.CC↗

arXiv2025

New Hybrid Heuristics for Pseudo-Boolean Propagation

In pseudo-boolean solving the currently most successful unit propagation strategy is a hybrid mode combining the watched literal scheme with the counting method. This short paper introduces new heuristics for this hybrid decision, which are able to drastically outperform the current method in the RoundingSAT solver.

cs.AI↗

arXiv2025

Complexity of chess domination problems

We study different domination problems of attacking and non-attacking rooks and queens on polyominoes and polycubes of all dimensions. Our main result proves that maximum independent domination is NP-complete for non-attacking queens and for non-attacking rooks on polycubes of dimension three and higher. We also analyze these problems for polyominoes and convex polyominoes, conjecture the complexity classes, and provide a computer tool for investigation. We have also computed new values for classical queen domination problems on chessboards (square polyominoes). For our computations, we have translated the problem into an integer linear programming instance. Finally, using this computational implementation and the game engine Godot, we have developed a video game of minimum domination of queens and rooks on randomly generated polyominoes.

math.CO↗

arXiv2023

There is no perfect Mondrian partition for squares of side lengths less than 1001

In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length $n$ square for $n\leq 1000$. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a $n \times m$ rectangle for $n,m \leq 400$.

math.CO↗